An encyclopedist of the dark ages: Isidore of Seville

by Ernest Brehaut

BOOK II

ON RHETORIC

INTRODUCTION

Rhetoric held a position in the ancient world that the modern reader has difficulty in understanding. Democratic government, including the popular administration of justice, at a time when all discussion was necessarily oral, created an ideal condition in Athens and the other Greek states for the development of oratory. In the life of the Roman republic, too, there was enough of the popular element to make public speaking of the greatest importance. The art of rhetoric was therefore in close touch with the real interests of life. It was not merely a school discipline, but a preparation for a definite activity that held a high place in the esteem of the people, and it embodied a set of sensible ideas on public speaking in which the tendency to over-elaboration and artificiality characteristic of scholastic disciplines was kept in check by the wholesome influences that came from practical application.

With the establishment of the Roman Empire public discussion of political matters quickly disappeared, and forensic oratory for the same reason tended to decline. Thus the chief element which had given vitality to ancient rhetoric was eliminated. Roman oratory, however, died hard. It nursed itself on various pretences and shows. Much of the old interest in oratory turned back on rhetoric, which was thus exposed to a double danger, as an educational discipline that had lost connection with practical life and as a subject that had become too fashionable. When once the new influence had gained headway a strong tendency to artificiality was revealed. Rhetoric became scholastic and ridiculously overburdened with classification and terminology; it grew more lifeless as it grew more systematic. Interest then gradually subsided. Treatises grew shorter and drier, and consisted largely of long lists of terms defined without critical understanding of their meaning. The subject now held its place by the mere force of authority.

This was the state of rhetoric in Isidore’s time, and his treatment reflects the condition to which it had been reduced. He says that “it is easy for the reader to admire but impossible to understand” the books on rhetoric, and, further, that when they are laid aside “all recollection vanishes.” From a writer with this attitude little need be expected. His few miserable pages, compared with Quintilian’s interesting treatise, measure fully the decline of rhetoric during the first six centuries A.D. What Isidore gives is merely a summary, so cursory and disjointed that it frequently cannot be understood without liberal reference to the fuller treatises of his predecessors.

In Isidore’s De Rhetorica practically the whole of Cassiodorus’ text-book on this subject is incorporated without acknowledgment. Two authorities, Victorinus and Cicero, are quoted,[190] but on referring to Cassiodorus it becomes plain that even here Isidore is merely copying his authority’s citation of authority. However his brief chapter on law cannot be paralleled in any extant treatise before his time and its insertion must be credited to his initiative.

ANALYSIS[191]

I.	Definition (ch. 1).
II.	Chief writers (ch. 2).
III.	Divisions (ch. 3).
	1.	Inventio.
	2.	Dispositio.
	3.	Elocutio.
	4.	Memoria.
	5.	Pronuntiatio.
IV.	The three kinds of cases (ch. 4).
	1.	Deliberativum.[192]
	2.	Demonstrativum.[193]
	3.	Judiciale.[194]
V.	The two-fold status of cases[195] (ch. 5).
	1.	Rationalis.
		a.	Conjectura.[196]
		b.	Finis.[197]
			(1)	Juridicialis.[198]
				(a)	Absoluta.[199]
				(b)	Assumptiva.[200]
					(a)	Concessio.[201]
							Purgatio.[202]
							Deprecatio.[203]
					(b)	Remotio criminis.[204]
					(c)	Relatio criminis.[205]
					(d)	Comparatio.[206]
			(2)	Negotialis.[207]
		c.	Qualitas.[208]
		d.	Translatio.[209]
	2.	Legalis.
		a.	Scriptum et voluntas.[210]
		b.	Leges contrariae.[211]
		c.	Ambiguitas.[212]
		d.	Collectio.[213]
		e.	Definitio legalis.[214]
VI.	The three-fold division of controversies[215] (ch. 6).
	1.	Simple.
	2.	Compound.
	3.	Complex.
VII.	The four parts of a speech[216] (ch. 7).
	1.	Exordium.
	2.	Narratio.
	3.	Argumentatio.
	4.	Conclusio.
VIII.	The five modes of cases[217] (ch. 8).
	1.	Honestum.
	2.	Admirabile.[218]
	3.	Humile.
	4.	Anceps.
	5.	Obscurum.
IX.	Argumentation (ch. 9).
	1.	Inductio.
	2.	Ratiocinatio.[219]
		a.	Enthymema.
		b.	Epicherema.
		c.	Mendacium.[220]
X.	Law[221] (ch. 10).
XI.	The sententious saying (ch. 11).
XII.	Confirmation and denial (ch. 12).
XIII.	Personification and expression of character (chs. 13–14).
XIV.	Kinds of subjects (ch. 15).
		Finitum.
		Infinitum.
XV.	Style and diction (ch. 16).
XVI.	The three ways of speaking (ch. 17).
		Humile.
		Medium.
		Grandiloquium.
XVII.	Parts of a sentence (ch. 18).
XVIII.	Faults to be avoided[222] (chs. 19–20).
XIX.	Figures[223] (ch. 21).

EXTRACTS

Chapter 1. On rhetoric and its name.

1. Rhetoric is the science of speaking well in civil questions for the purpose of persuading to what is just and good. It is called rhetoric in the Greek ἀπὸ τοῦ ῥητορίζειν, that is, from eloquence of speech. For speech among the Greeks is called ῥῆσις, and the orator ῥήτωρ.

2. Rhetoric is allied to the grammatic art. For in grammar we learn the science of speaking correctly, and in rhetoric we discover in what way to express what we have learned.

Chapter 2. On the discoverers of the art of rhetoric.

1. This discipline was invented by Gorgias, Aristotle and Hermagoras among the Greeks, and translated into Latin by Tullius and Quintilian, but with such eloquence and variety that it is easy for the reader to admire, impossible to understand.

2. For while he holds the parchment the connected discourse as it were cleaves to his memory, but presently when it is laid aside all recollection vanishes. Perfect knowledge of this discipline makes the orator.

Chapter 3. On the name of the orator and the parts of rhetoric.

1. The orator is the good man skilled in speaking. ‘The good man’ means nature, character, accomplishments (artibus). ‘Skilled in speaking’ means studied eloquence, which consists of five parts: invention, ordering, diction and style, memory, delivery, and the purpose, which is to persuade of something.

2. Skill in speaking consists in three things: nature, learning, practise; nature, that is, talent; learning, knowledge; practice, continuous labor. These are the things that are looked to not only in the orator but in every artist with a view to accomplishment.

Chapter 4. The three kinds of causes.

1. There are three kinds of causes: deliberative, epideictic, judicial. The deliberative kind is that in which there is a discussion as to what ought or ought not to be done in regard to any of the practical affairs of life. The epideictic, in which a character is shown to be praiseworthy or reprehensible.

2. The judicial, in which opinion as to reward or punishment with reference to an act of an individual is given.

Chapter 16. Style and diction.

2. One must use good Latin and speak to the point. He speaks good Latin who constantly uses the true and natural names of things, and is not at variance with the style and literary refinement of the present time. Let it not be enough for him to be careful of what he says, without saying it in a clear, attractive manner; nor that only, without saying what he says wittily also.

Chapter 21. On figures.

1. Speech is amplified and adorned by the use of figures. Since direct, unvaried speech creates a weariness and disgust both of speaking and hearing, it must be varied and turned into other forms, so that it may give renewed power to the speaker, and become more ornate and turn the judge from an aloof countenance and attention.

ON DIALECTIC

INTRODUCTION

In tracing the fortunes of logic through the period of decadence and the dark ages the effect upon it of a transition from a pagan to a Christian environment need scarcely be taken into consideration. Such marks of degeneration as it shows must be attributed simply to the general decay of thought, which was marked in both pagan and Christian spheres. By its character logic was well adapted to pass from the service of Greek philosophy and science to that of Christian theology: it had been worked out mainly as a method of Greek science, which was especially backward in the fields where induction plays a large part; consequently the Greek logic is not inductive. It is the logic of universals ready-made, and it has nothing to do with their making; it receives universals as authoritative. It was therefore most welcome to Christian thinkers, since it was precisely adapted to “the task of drawing out the implications of dogmatic premises.”[224]

It was not until a very late period that logic appeared in the Latin language in the form of a school text. In fact, with the exception of Varro’s Dialectic in his “Nine Books of the Disciplines,” which has been lost, there were no writings on logic in the Latin down to the fourth century. Instruction in the subject was apparently given in Greek and to but few pupils. In the fourth century, however, Greek was going out of use, and it became necessary, if logic was to be saved in the schools, to have Latin text-books.[225] The need was met by a line of text-writers, of whom Marius Victorinus (c. 350) was the first. The oldest Latin school-book on logic that has survived, however, is that of Martianus Capella. Neither he nor his two successors, Cassiodorus and Isidore, were versed in the subject; they were merely compilers of educational encyclopedias. Such was the perfunctory origin of the Latin text-books on logic.[226]

The reader of Isidore’s account of logic is struck by the enthusiasm displayed. Speaking of Aristotle’s Categories he says: “This work of Aristotle’s should be read attentively, since, just as is stated therein, all that a man says is included in the ten categories.”[227] Further on he quotes the saying that “Aristotle dipped his pen in intellect when he wrote the Perihermeniae.”[228] Again, a study of Apuleius “will introduce the reader advantageously with God’s help to great paths of understanding.”[229] All of these passages, however, come word for word from Cassiodorus. Isidore’s enthusiasm as well as his bibliography seems to lack genuineness.[230]

ANALYSIS

I.	Definition of dialectic (chs. 22, 23).
	1.	Distinction between dialectic and rhetoric.
II.	Definition of philosophy (ch. 24).
III.	The Isagoges[231] of Porphyry (ch. 25).
	1.	The five predicables: genus, species, differentia, proprium, accidens.
IV.	The Categories of Aristotle (ch. 26).
V.	Aristotle’s De perihermeniis[231] (ch. 27).
	1.	Thought as expressed in language.
VI.	The syllogisms (ch. 28).
	1.	Categorical syllogisms.
	2.	Hypothetical syllogisms.
VII.	Definition (ch. 29).
	The fifteen kinds of definition.
VIII.	Arguments (topica) (ch. 30).
	The twenty-two loci of arguments.
IX.	Opposites (ch. 31).

EXTRACTS

Book II, Chapter 22. On dialectic.

1. Dialectic is the discipline elaborated with a view of ascertaining the causes of things. In itself it is the sub-division of philosophy that is called logical, i.e., rational, capable of defining, enquiring and expressing precisely. For it teaches in the several kinds of questions how the true and false are separated by discussion.

2. The first philosophers used dialectic in their discourses, but they did not reduce it to the practical form of an art. After them Aristotle systematized the subject-matter of this branch of learning, and called it dialectic, because there is discussion of words (dictis) in it; for λεκτὸν means dictio. And dialectic follows after the discipline of rhetoric because they have many things in common.

Chapter 23. On the difference between the dialectical and the rhetorical art.

1. Varro, in the nine books of the Disciplinae, distinguished dialectic and rhetoric by the following simile: “Dialectic and rhetoric are as in man’s hand the closed fist and the open palm, the former drawing words together, the latter scattering them.”

2. If dialectic is keener in expressing things precisely, rhetoric is more eloquent in persuading to the belief it desires. The former seldom appears in the schools, the latter goes without a break [from the schools] to the law-court. The former gets few students, the latter often whole peoples.

3. Before they come to the explanation of the Isagoge, philosophers are wont to give a definition of philosophy, in order that the things which concern it may be shown more easily.

Chapter 24. On the definition of philosophy.

1. Philosophy is the knowledge of things human and divine, united with a zeal for right living. It seems to consist of two things, knowledge and opinion.

2. It is knowledge when anything is known with definiteness; opinion, when a thing lurks as yet in uncertainty and seems in no way established, as for example, whether the sun is [only] as large as it seems or greater than all the earth; likewise whether the moon is a sphere or concave; and whether the stars adhere to the heavens or pass in free course through the air; of what size the heaven itself is and of what material it is composed; whether it is quiet and motionless or revolves with incredible speed; how great is the thickness of the earth, or on what foundations it continues poised and supported.

3. The word philosophy, translated into Latin, means amor sapientiae. For the Greeks call amor φιλὸν, and sapientiae σοφίαν. The sub-division of philosophy is three-fold: first, natural philosophy, which in Greek is called physica, in which there is discussion of the search into nature; the second, moral, which in Greek is called ethica, in which the subject is morals; the third, rational, which in the Greek is called logica, in which the discussion is as to how the truth itself is to be sought in respect to the causes of things or the conduct of life.

4. In physics, then, the cause of inquiry, in ethics, the manner of living, in logic, the method of understanding, are concerned. Among the Greeks, Thales of Miletus, one of the seven wise men, was the first to search into natural philosophy. For this man first regarded with contemplative thought the causes of the heavens and the force of the things of nature. And this division of philosophy Plato afterward divided into four separate parts, namely, into arithmetic, geometry, music, astronomy.

5. Socrates first established ethics with a view to correcting and ordering conduct, and he devoted all his attention to the discussion of right living, dividing it into the four virtues of the soul, namely, wisdom, justice, fortitude, temperance.

6. Wisdom is engaged with things, and by it the evil is distinguished from the good. Fortitude, by which adversity is endured with calmness. Temperance, by which lust and concupiscence are bridled. Justice, by which through righteous judgment his own is rendered to each.

7. Plato added logical philosophy, which is called rational, and by it he analyzed the causes of things and of conduct, and examined their force in a rational way, dividing it into dialectic and rhetoric. It is called logical, that is, rational, for among the Greeks λόγος means both word and reason.

8. The divine utterances also consist of these three kinds of philosophy. For they are wont to discuss nature, as in Genesis or Ecclesiastes; or conduct, as in Proverbs and here and there in all the books; or logic, instead of which our [philosophers] assert the claim of theology,[232] as in the Song of Songs or the Gospels.

9. Likewise some of the teachers have defined philosophy in its name and parts as follows: “Philosophy is the probable knowledge of divine and human affairs, as far as is possible for man.” Otherwise: “Philosophy is the art of arts and the science of sciences.” Again: “Philosophy is the meditation upon death, a definition which better suits the Christians, who trampling on worldly ambition, live in the intercourse of learning after the likeness of their future country.”

10. Others have defined the scheme of philosophy as made up of two parts, of which the former is contemplative, the latter practical. The contemplative (inspectiva) is divided into natural, theoretical, and divine. Theoretical is divided into four parts, into arithmetic, music, geometry, and astronomy.

11. Practical (actualis) philosophy is divided into moral, economic, and civil. Contemplative is the name given that in which, passing beyond the visible, we enjoy some contemplation of the divine and celestial, and behold them with the mind alone, since they pass beyond the bodily gaze.

12. Natural philosophy is the name given when the nature of each and every thing is discussed, since nothing arises contrary to nature in life, but each thing is assigned to those uses for which it was purposed by the Creator, unless perchance by God’s will it is shown that some miracle appears.

13. It is called divine philosophy when we discuss the ineffable nature of God or the spiritual beings that are in some degree of a lofty nature.

14. The science which considers abstract quantity is called theoretical. For that is called abstract quantity which we separate from the material, or from other accidents, by the intellect, and treat by reasoning alone, as e.g., equal, unequal, and other matters of this kind....

16. Further, that is called practical philosophy which by its workings makes problems clear, of which there are three parts, moral, economic, and civil. That is called moral by which an honorable custom (mos) of living is sought and practices tending to virtue are established. That is called economic (dispensativa) in which the order of domestic affairs is wisely arranged. That is called civil by which the advantage of a whole state is secured.

Chapter 25. On the Isagoges of Porphyry.

1. After the definitions of philosophy in which all things are embraced under general heads, let us now describe the Isagoges of Porphyry. Isagoge in the Greek means introductio in the Latin, being meant for those, it is plain, who are beginning philosophy, and containing an explanation of first principles. In regard to anything whatever it is made clear what its nature is, by unfailing definition of the substance.

2. For setting down first the genus, then the species, we subjoin also other things that are possibly related, and by setting aside common qualities we make distinctions, continually interposing differences until we arrive at the proper quality of that which we are examining, its meaning being made definite, as, for example: Homo est animal rationale, mortale, terrenum, bipes, risus capax.

3. When the genus animal is mentioned the substance of man is declared. For with reference to man the genus is animal; but since it has a wide application, the species, terrenum, is added and now what belongs to the air or water is excluded. And a difference is added, as, for example, bipes, which is given on account of the animals that go on several feet. Likewise rationale, because of the animals which lack reason; and mortale, because man is not an angel.

4. Afterwards, when the common qualities had been set aside, the property was added at the end, for it is the characteristic of man alone to laugh. In this way the complete definition to indicate man was reached. Aristotle and Tully held that the full definition of this science consisted of genus and differences.

5. Later certain authorities, expressing their position more fully, in their teaching divided perfect substantial definition into five divisions, as if into five organic parts. And the first of these deals with genus, the second with species, the third with difference, the fourth with proper quality, the fifth with accident.

Chapter 26. On the categories of Aristotle.

1. Next follow the categories of Aristotle, which in Latin are called praedicamenta, within which all discourse is embraced throughout its various meanings.

5. There are ten sorts of categories, namely, substantia, quantitas, qualitas, relatio, situs, locus, tempus, habitus, agere, pati.

15. This work of Aristotle ought to be read with attention, since, as has been observed, whatever man speaks is included within the ten categories. It will help also to the understanding of the books that are devoted either to rhetoric or to logic.[233]

Chapter 27. On Interpretation (de Perihermeniis).

1. There follows next the book On Interpretation, which is extremely subtle and guarded in its various formulas and repetitions, of which it is said: “Aristotle when he wrote the Perihermeniae dipped his pen in intellect.”

Chapter 28. On syllogisms.

1. Next follow the syllogisms of dialectic, wherein the advantage and excellence of that whole art is exhibited, the inferences of which greatly aid the reader in searching out the truth, so that the common error of deceiving an adversary by the sophisms of false conclusions disappears.

2. There are three formulae of categorical syllogisms. To the first formula belong nine modes....

12. To the second formula belong four modes....

16. To the third formula belong six modes.

22. Let him who desires to understand fully these formulas of the categorical syllogisms read the book entitled Apuleii Perihermeniae, and he will learn matters that are treated with subtlety.[234] And by their clearness and well-weighed character they will introduce the reader advantageously with God’s help to great paths of understanding. Now let us come to the hypothetical syllogisms in order.

23–25. The modes of the hypothetical syllogisms that have a conclusion are seven.... If anyone desires to know more fully the modes of the hypothetical syllogisms let him read Marius Victorinus’ book entitled De Syllogismis Hypotheticis.[234]

26. Next let us approach the topic of dialectical definitions, which have such surpassing worth that they may rightly be called the clear manifestations of speech, and in a sense the guides to expression.

Chapter 29. On the division of definitions, abbreviated from the book of Marius Victorinus.

1. The definition of the philosophers is that which in describing things sets forth what the thing in itself is—not, of what sort it is—and how it ought to be made up of its parts. For it is a brief statement separating the nature of each thing from its class, and marking it off by its peculiar meaning. Definitions are divided into fifteen sorts. The first kind of definition is the substantial (οὐσιώδης), which is named definition in the proper and true sense, as, for example, Est homo animal rationale, mortale, risus disciplinaeque capax. This definition descends through species and differences and comes to the property, and expresses most fully what man is.

16. Now let us come to the topica, which are the seats of arguments, the fountains of ideas, and the sources of speech.

Chapter 30. On the topics.

1. Topica is the science of finding arguments. The division of the topica or the loci from which arguments are derived is three-fold. For some inhere in the very thing that is under discussion; there are others, called affecta (closely connected), which are known to be derived in a certain sense from other things; others, which are taken from outside [the subject]....

18. It is clearly a wonderful thing that whatever the nimbleness and variety of the human mind could discover, searching for ideas in different cases, could have been gathered into unity; that free and spontaneous intelligence is limited. For wherever it turns, whatever thoughts it enters on, the mind must fall upon some of those that have been described.

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BOOK III

On the Four Mathematical Sciences

ON ARITHMETIC

INTRODUCTION

In examining Isidore’s De Arithmetica two peculiarities of the development of the subject should be borne in mind. In the first place, the predominant position among the mathematical sciences which Isidore claims for arithmetic was one acquired by it comparatively late. Owing perhaps to the awkwardness of the Greek notation of number[235] geometry had been developed first, and historically arithmetic was an off-shoot from geometry and borrowed its terminology largely from it.[236] It was not given an independent form until the time of Nicomachus (fl. 100 A.D.) whose Introductio Arithmetica was “the first exhaustive work in which arithmetic was treated quite independently of geometry.”[237] Once it become independent, arithmetic, instead of geometry, came to be regarded as the fundamental mathematical science. The old tradition is reflected in Martianus Capella’s order of subjects, in which geometry is placed first and arithmetic second, while the newer tradition is seen in the order of Cassiodorus and Isidore, who both have passages also emphasizing the fundamental character of arithmetic.

The second peculiarity is one which will surprise the modern reader who is familiar with arithmetic as a utilitarian study. The ancient arithmetica had nothing to do with the art of reckoning, which was called logistica.[238] The science and the art of numbers were completely divorced and the latter was excluded from the higher education as we have it in the seven liberal arts. Consequently we can expect nothing practical in Isidore’s De Arithmetica. Nothing is said of methods of calculation, elementary or advanced, and, as a matter of course, nothing is to be found here on such topics as the use of the abacus[239] or the method of computing Easter, though the latter was the greatest mathematical problem of the time.

Isidore’s source in the De Arithmetica was Cassiodorus,[240] whom he copies with little change; while Cassiodorus’ work was apparently a bare abstract of Boethius’ translation of Nicomachus. Isidore’s account is of great brevity and contains a number of unexplained technical terms.

EXTRACTS

Preface. Mathematics is called in Latin doctrinalis scientia. It considers abstract quantity. For that is abstract quantity which we treat by reason alone, separating it by the intellect from the material or from other non-essentials, as for example, equal, unequal, or the like. And there are four sorts of mathematics, namely, arithmetic, geometry, music and astronomy. Arithmetic is the science of numerical quantity in itself. Geometry is the science of magnitude and forms.[241] Music is the science that treats of numbers that are found in sounds. Astronomy is the science that contemplates the courses of the heavenly bodies and their figures, and all the phenomena of the stars. These sciences we shall next describe at a little greater length in order that their significance may be fully shown.

Chapter 1. On the name of the science of arithmetic.

1. Arithmetic is the science of numbers. For the Greeks call number ἀριθμός. The writers of secular literature have decided that it is first among the mathematical sciences since it needs no other science for its own existence.

2. But music and geometry and astronomy, which follow, need its aid in order to be and exist.

Chapter 2. On the writers.

1. They say that Pythagoras was the first among the Greeks to write of the science of number, and that it was later described more fully by Nicomachus, whose work Apuleius first, and then Boethius, translated into Latin.

Chapter 3. What number is.

1. Number is multitude made up of units. For one is the seed of number but not number. Nummus (coin) gave its name to numerus (number), and from being frequently used originated the word.

Unus derives its name from the Greek, for the Greeks call unus ἕνα, likewise duo, tria, which they call δύο and τρία.

2. Quattuor took its name from a square figure (figura quadrata). Quinque, however, received its name from one who gave the names to numbers not according to nature but according to whim. Sex and septem come from the Greek.

3. For in many names that are aspirated in Greek we use s instead of the aspiration. We have sex for ἑξ, septem for ἕπτα, and also the word serpillum (thyme) for herpillum. Octo is borrowed without change; they have ἔννεα, we novem; they δέκα, we decem.

4. Decem is so-called from a Greek etymology, because it ties together and unites the numbers below it. For to tie together and unite is called among them δεσμεύειν.[242]

Chapter 4. What numbers signify.

1. The science of number must not be despised. For in many passages of the holy scriptures it is manifest what great mystery they contain. For it is not said in vain in the praises of God: “Omnia in mensura et numero et pondere fecisti.” For the senarius, which is perfect in respect to its parts,[243] declares the perfection of the universe by a certain meaning of its number. In like manner, too, the forty days which Moses and Elias and the Lord himself fasted, are not understood without an understanding of number.

3. So, too, other numbers appear in the holy scriptures whose natures none but experts in this art can wisely declare the meaning of. It is granted to us, too, to depend in some part upon the science of numbers, since we learn the hours by means of it, reckon the course of the months, and learn the time of the returning year. Through number, indeed, we are instructed in order not to be confounded. Take number from all things and all things perish. Take calculation from the world and all is enveloped in dark ignorance, nor can he who does not know the way to reckon be distinguished from the rest of the animals.

Chapter 5. On the first division into even and odd.

1. Number is divided into even and odd. Even number is divided into the following: evenly even, evenly uneven, and unevenly even, and unevenly uneven.[244] Odd number is divided into the following: prime and uncompounded, compounded, and a third class which comes between (mediocris) which in a certain way is prime and uncompounded, but in another way secondary and compounded.

2. An even number is that which can be divided into two equal parts, as II, IV, VIII.[245] An odd number is that which cannot be divided into equal parts, there being one in the middle which is either too little or too much, as III, V, VII, IX, and so on.

3. Evenly even number is that which is divided equally into even number, until it comes to indivisible unity, as for example, LXIV has a half XXXII, this again XVI; XVI, VIII; VIII, IV; IV, II; II, I, which is single and indivisible.

4. Evenly uneven is that which admits of division into equal parts, but its parts soon remain indivisible, as VI, X, XVIII, XXX, and L, for presently, when you divide such a number, you run upon a number which you cannot halve.

5. Unevenly even number is that whose halves can be divided again, but do not go on to unity, as XXIV. For this number being divided in half makes XII, divided again VI, and again, III; and this part does not admit of further division, but before unity a limit is found which you cannot halve.

6. Unevenly uneven is that which is measured unevenly by an uneven number, as XXV, XLIX; which, being uneven numbers, are divided also by uneven factors, as, seven times seven, XLIX, and five times five, XXV. Of odd numbers some are prime, some compounded, some mean (mediocris).

7. Prime numbers are those which have no other factor except unity alone, as three has only a third, five only a fifth, seven only a seventh, for these have only one factor.

Compound numbers are they which are not only measured by unity, but are produced by another number, as IX, XV, XXI, XXV. For we say three times three are nine, and seven times three are XXI, and three times five are XV, and five times five are XXV.

8. Mean (mediocris) numbers are those which in a certain fashion seem prime and uncompounded and in another fashion secondary and compounded. For example, when IX is compared with XXV, it is prime and uncompounded, because it has no common factor except unity alone, but if it is compared with XV it is secondary and compounded, since there is in it a common factor in addition to unity, that is, III. Because three times three make nine, and three times five make fifteen.[246]

9. Likewise of even numbers some are excessive, others defective, others perfect.[247] Excessive are those whose factors being added together exceed its total, as for example, XII. For it has five factors: a twelfth, which is one; a sixth, which is two; a fourth, which is three; a third, which is four; a half, which is six. For one and two and three and four and six being added together make XVI, which is far in excess of twelve....

10. Defective numbers are those which being reckoned by their factors make a less total, as for example, ten....

11. The perfect number is that which is equalled by its factors, as VI.... The perfect numbers are, under ten, VI; under a hundred, XXVIII; under a thousand, CCCCXCVI.

Chapter 6. On the second division of all number.

1. All number is considered either with reference to itself or in relation to something. The former is divided as follows: some are equal, as for example, two; others are unequal, as for example, three.[248] The latter is divided as follows: some are greater, some are less. The greater are divided as follows: into multiplices (multiple), superparticulares, superpartientes, multiplices superparticulares, multiplices superpartientes. The less are divided as follows: Sub-multiplices (sub-multiple), sub-superparticulares, sub-superpartientes, sub-multiplices sub-superparticulares, sub-multiplices sub-superpartientes.

6. ... The superparticularis numerus is when a greater number contains in itself a lesser number with which it is compared, and at the same time one part of it.

7. For example; III when compared with II contains in itself two and also one, which is the half of two. IV when compared with III, contains three and also one, which is the third of three. Likewise V, when compared with IV, contains the number four and also one, which is the fourth part of the said number four, and so on.

8. The superpartiens numerus is that which contains the whole of a lesser number and in addition two parts of it, either thirds or fifths or other parts. For example, when V is compared with III, the number five contains three and in addition to this two parts of it.

Chapter 7. On the third division of all number.

1. Numbers are abstract or concrete. The latter are divided as follows: first, lineal; second, superficial; third, solid. Abstract number is that which is made up of abstract units. For example, III, IV, V, VI, and so on.

2. Concrete number is that which is made up of units that are not abstract, as for example, the number three, if it is understood of magnitude, whether line, superficies, or solid, is called concrete.

4. The number of superficies is that which is constituted not only by length but also by breadth, as triangular, square, pentangular, or circular numbers, and the rest that are contained in a plane surface or superficies.

5. The circular number, when it is multiplied by itself, beginning with itself, ends with itself. For example, Quinquies quini vicies quinque.

6. ... The spherical number is that which being multiplied by the circular number begins with itself and ends with itself; for example, five times five are twenty-five, and this circle being multiplied by itself makes a sphere, that is, five times XXV make CXXV.

Chapter 8. On the distinction between arithmetic, geometry, and music.

1. Between arithmetic, geometry and music there is a difference in finding the means. In arithmetic in the first place you find it in this way. You add the extremes and divide and find the half; as for example, suppose the extremes are VI and XII, you add them and they make XVIII. You divide and get IX, which is the mean of arithmetic (analogicum arithmeticae), since the mean is surpassed by the last by as many units as it surpasses the first. For IX surpasses VI by three units, and XII surpasses it by the same number.

2. According to geometry you find it this way. The extremes multiplied together make as much as the means multiplied, for example, VI and XII multiplied make LXXII; the means VIII and IX multiplied make the same.

3. According to music you find it in this way: The mean is exceeded by the last term by the part by which it exceeds the first term, as for example, VI is surpassed by VIII by two units, which is a third part, and by the same part the mean VIII is surpassed by the last term which is XII.

Chapter 9. That infinite numbers exist.

1. It is most certain that there are infinite numbers, since at whatever number you think an end must be made I say not only that it can be increased by the addition of one, but, however great it is, and however large a multitude it contains, by the very method and science of numbers it can not only be doubled but even multiplied.

2. Each number is limited by its own proper qualities, so that no one of them can be equal to any other. Therefore in relation to one another they are unequal and diverse, and the separate numbers are each finite, and all are infinite.

ON GEOMETRY

INTRODUCTION

In spite of the high development of geometry among the Greeks it never took root as a pure science in the western Roman world,[249] and neither the various practical applications of its principles nor its use as a disciplinary educational subject sufficed to fasten thoughtful attention upon it; in consequence, it lost almost its entire content. As it appears in the four writers who treat of it in later Roman and early medieval times, Martianus Capella, Boethius,[250] Cassiodorus, and Isidore, it furnishes a striking commentary upon the intellectual conservatism that could retain without a suspicion of criticism a subject that was no longer anything but empty form.

The substance of Isidore’s De Geometria comes with little change from Cassiodorus. It is noteworthy that these two writers have nothing that does not go with the subject according to the modern conception of it, and do not follow the example of their predecessor Martianus Capella,[251] in whose account of the seven liberal arts the void caused by the loss of the proper content of geometry is filled with geography.

TRANSLATION[252]

Book III, Chapter 10. On the inventors of geometry and its name.

1. The science of geometry is said to have been discovered first by the Egyptians, because when the Nile overflowed and all their lands were overspread with mud, its origin in the division of the land by lines and measurements gave the name to the art. And later, being carried further by the keenness of the philosophers, it measured the spaces of the sea, the heavens, and the air.

2. For, having their attention aroused, students began to search into the spaces of the heavens, after measuring the earth; how far the moon was from the earth, the sun itself from the moon, and how great a measure extended to the summit of the sky; and thus they laid off in numbers of stades with probable reason the very distances of the sky and the circuit of the earth.

3. But since this science arose from the measuring of the earth, it took its name also from its beginning. For geometria is so named from the earth and measuring. For the earth is called γῆ in Greek, and measuring, μέτρον. The art[253] of this science embraces lines, intervals, magnitudes, and figures, and in figures, dimensions and numbers.

Chapter 11. On the four-fold division of geometry.

1. The four-fold division of geometry is into plane figures, numerical magnitude, rational magnitude, and solid figures.

2. Plane figures are those which are contained by length and breadth. Numerical magnitude is that which can be divided by the numbers of arithmetic.

3. Rational magnitudes are those whose measures we can know, and irrational, those the amount of whose measurement is not known.

4. Solid figures are those that are contained by length, breadth, and thickness, which are five in number, according to Plato.

Chapter 12. On the figures of geometry.

1. The first of the figures on a plane surface is the circle, a figure that is plane, and has a circumference, in the middle of which is a point upon which everything converges (cuncta convergunt) which geometers call the center, and the Latins call the point of the circle.

2. A quadrilateral figure is one on a plane surface, and it is contained by four straight lines....

3. A sphere is a figure of rounded form equal in all its parts.

A cube is a solid figure which is contained by length, breadth, and thickness.

5. A cone (conon) is a solid figure which narrows from a broad base like the right-angled triangle.

6. A pyramid is a solid figure which narrows to a point from a broad base like fire. For fire in Greek is called πῦρ.

7. Just as all number is contained within ten so the outline of every figure is contained within the circle.

Chapter 13. On the first principles of geometry.

1. ... A point is that which has no part. A line is length without breadth. A straight line is one which lies evenly in respect to its points. A superficies is that which has length and breadth alone.

Chapter 14. On the numbers of geometry.

1. You search into the numbers of geometry as follows: the extremes being multiplied, amount to as much as the means multiplied; as for example, VI and XII being multiplied, make LXXII; the means VIII and IX being multiplied, amount to the same.

ON MUSIC

INTRODUCTION

As an educational subject music is the oldest of those grouped under the heading of the seven liberal arts. In Plato’s time music and gymnastic were the staples of education, and the former term meant chiefly the study of poetry, with music in the proper sense of the word as a mere adjunct. As the different subjects, such as grammar, rhetoric, geometry, arithmetic, appeared in the curriculum, the field of music narrowed and it held a less commanding place. Conflicting points of view in regard to it appear to have arisen. The older educational tradition connected music with grammar and the other literary studies. On the other hand, the influence of the Pythagorean theory of number and of its application to music tended to dissociate grammar and music, and to place the latter in relation to the mathematical sciences. It has been noticed that among the older Roman writers from whom evidence on this matter can be drawn—Cicero, Varro, Seneca, Quintilian, and others—the association of music and grammar appears the natural one, while in the Roman writers of the second, third, and fourth centuries both traditions prevail, with an increasing preference for placing music among the mathematical sciences, where it finally found itself when the canon of the seven liberal arts was formed, and where it remained to the end of the middle ages.[254]

In Isidore little is to be found to justify the mathematical environment of music. It is true that at times he defines it as a mathematical science[255] and he insists on the musical view of the universe as a necessary complement to other views. “Without music,” he says, “there can be no perfect knowledge, for there is nothing without it. For even the universe itself is said to have been formed under the guidance of harmony.”[256] But, with the exception of a paragraph on the musical mean, his treatment is entirely taken up with the non-mathematical aspect of the subject, and the definition “music is the practical knowledge of melody”[257] is the one that more closely fits the occasion.

The treatment[258] of music is of about the same length as that of arithmetic, and is devoted mainly to definitions of musical terms and brief descriptions of wind and stringed instruments. It appears that Isidore knew nothing of music in a technical sense.[259]

EXTRACTS

Book III, Chapter 15. On music and its name.

1. Music is the practical knowledge of melody, consisting of sound and song; and it is called music by derivation from the Muses. And the Muses were so-called ἀπὸ τοῦ μῶσθαι, that is, from inquiring, because it was by them, as the ancients had it, that the potency of songs and the melody of the voice were inquired into.

2. Since sound is a thing of sense it passes along into past time, and it is impressed on the memory. From this it was pretended by the poets that the Muses were the daughters of Jupiter and Memory. For unless sounds are held in the memory by man they perish, because they cannot be written.

Chapter 16. On its discoverers.

1. Moses says that the discoverer of the art of music was Jubal, who was of the family of Cain and lived before the flood. But the Greeks say that Pythagoras discovered the beginnings of this art from the sound of hammers and the striking of tense cords. Others assert that Linus of Thebes, and Zethus, and Amphion, were the first to win fame in the musical art.

2. After whose time this science in particular was gradually established and enlarged in many ways, and it was as disgraceful to be ignorant of music as of letters. And it had a place not only at sacred rites, but at all ceremonies and in all things glad or sorrowful.

Chapter 17. On the power of music.

1. And without music there can be no perfect knowledge, for there is nothing without it. For even the universe itself is said to have been put together with a certain harmony of sounds, and the very heavens revolve under the guidance of harmony. Music rouses the emotions, it calls the senses to a different quality.

2. In battles, too, the music of the trumpet fires the warriors, and the more impetuous its loud sound the braver is the spirit for the fight. Also, song cheers the rowers. For the enduring of labors, too, music comforts the mind, and singing lightens weariness in solitary tasks.

3. Music calms overwrought minds also, as is read of David, who by his skill in playing rescued Saul from an unclean spirit. Even the very beasts and snakes, birds and dolphins, music calls to hear its notes. Moreover whatever we say or whatever emotions we feel within from the beating of our pulses, it is proven that they are brought into communion with the virtues through the musical rhythms of harmony.

Chapter 18. On the three parts of music.

1. There are three parts of music, namely, harmonica, rhythmica, metrica. Harmonica is that which distinguishes in sounds the high and the low. Rhythmica is that which inquires concerning the succession of words as to whether the sound fits them well or ill.

2. Metrica is that which learns by approved method the measure of the different metres, as for example, the heroic, iambic, elegiac, and so on.

Chapter 19. On the triple division of music.

1. It is agreed that all sound which is the material of music is of three sorts. First is harmonica, which consists of vocal music; second is organica, which is formed from the breath; third is rhythmica, which receives its numbers from the beat of the fingers.

2. For sound is produced either by the voice, coming through the throat; or by the breath, coming through the trumpet or tibia, for example; or by touch, as in the case of the cithara or anything else that gives a tuneful sound on being struck.

Chapter 20. On the first division of music which is called harmonica.

1. The first division of music, which is called harmonica, that is, modulation of the voice, has to do with comedians, tragedians, and choruses, and all who sing with the proper voice.[260] This [coming] from the spirit and the body makes motion, and out of motion, sound, out of which music is formed, which is called in man the voice.

2. Harmonica is the modulation of the voice and the concord or fitting together of very many sounds.

3. Symphonia is the managing of modulation so that high and low tones accord, whether in the voice or in wind or stringed instruments. Through this, higher and lower voices harmonize, so that whoever makes a dissonance from it offends the sense of hearing. The opposite of this is diaphonia, that is, voices grating on one another or in dissonance.

7. Tonus is a high utterance of voice. For it is a difference and measure of harmony which depends on the stress and pitch of the voice. Musicians have divided its kinds into fifteen parts, of which the hyperlydian is the last and highest, the hypodorian the lowest of all.

8. Song is the modulation of the voice, for sound is unmodulated, and sound precedes song.

Chapter 21. On the second division, which is called organica.

1. The second division, organica, has to do with those [instruments] that, filled with currents of breath, are animated so as to sound like the voice, as for example, trumpets, reeds, Pan’s pipes, organs, the pandura, and instruments like these.[261]

Chapter 22. On the third division, which is called rhythmica.

1. The third division is rhythmica, having to do with strings and instruments that are beaten, to which are assigned the different species of cithara, the drum, and the cymbal, the sistrum, acitabula of bronze and silver, and others of metallic stiffness that when struck return a pleasant tinkling sound, and the rest of this sort.[262]

2. The form of the cithara in the beginning is said to have been like the human breast, because as the voice was uttered from the breast so was music from the cithara, and it was so-called for the same reason. For pectus is in the Doric language called κίθαρα.

Chapter 23. On the numbers of music.

1. You inquire into the numbers according to music as follows: setting down the extremes, as for example, VI and XII, you see by how many units VI is surpassed by XII, and it is by VI units; you square it; six times six make XXXVI. You add those first-mentioned extremes, VI and XII; together they make XVIII; you divide XXXVI by XVIII; two is the result. This you add to the smaller amount, VI namely; the result will be VIII and it will be the mean between VI and XII. Because VIII surpasses VI by two units, that is by a third of six, and VIII is surpassed by XII by four units, a third part [of twelve]. By what part, then, the mean surpasses, by the same is it surpassed.

2. Just as this proportion exists in the universe, being constituted by the revolving circles, so also in the microcosm—not to speak of the voice—it has such great power that man does not exist without harmony.[263]

ON ASTRONOMY

INTRODUCTION

The science of astronomy, in its history from the great period of Greece down to the dark ages, furnishes almost as complete a spectacle of decay as does geometry. It is quite certain “that Aristarchus taught the annual motion of the earth around the sun, and both he and Seleukus taught the diurnal rotation of the earth,”[264] but the general scientific development of the age was not sufficient to assimilate this advanced theory, and astronomers went back to a geocentric universe. Strange to say, the later rise of practical astronomy at Alexandria, and the development of pure mathematics, did not secure a return to the more advanced theory, the efforts of the later astronomers being devoted, not to a reconsideration of the fundamental theses of the subject, but to putting the geocentric theory on a secure mathematical basis. The greatest of these astronomers, Ptolemy (second century A.D.), left in his Syntaxis a comprehensive summing up of mathematical astronomy.

Among the Romans no scientists arose to assimilate the results of the work of the Greeks, and sound ideas as to the form of the universe were rare even in the most intelligent circles. Since systematic observation was not practiced, and a knowledge of the higher mathematics did not exist among the Romans, their astronomy was a matter of tradition and authority. Therefore upon the acceptance of Christianity and the realization that there was a conflict between the Greek and the Hebrew cosmologies, it was a comparatively easy matter to accept the Scriptures instead of the secular writers as the source of authority.

In Isidore’s ideas on cosmology a curious inconsistency appears. On the one hand, he shows that he regards the words of the Scripture as the final authority, and he frequently gives expression to primitive notions in accord with the Hebrew cosmology. On the other hand, he displays a greater liberality than is shown by his predecessor, Cassiodorus, or by any other Christian writer in the Latin language up to his time, in borrowing from the pagan writers on astronomy. The explanation of this may be that it was a natural reaction from dogmatic narrowness, made possible for him by the favorable conditions offered by contemporary Spain; but the more probable supposition is that his natural vagueness of mind and lack of critical power enabled him to be much more liberal in effect than he in reality would have wished to be.[265]

Another feature of Isidore’s De Astronomia that deserves notice is his attitude toward the forbidden science of astrology.[266] He denies a fundamental assumption of the science, namely, that Mercury and Venus, for example, have as planets an influence analogous to their characters in mythology, and he asserts that the names of the planets and fixed stars, as used in astrology, have no validity. This was vigorous reasoning for the dark ages, and to all appearance it completely cut away the foundation of astrology.[267] Nevertheless Isidore believed that astrology had some truth—the magi who announced the birth of Christ were, he believed, astrologers—but this truth arose “out of a deadly alliance of men and bad angels.” His attitude, then, seems to be that astrologers may forecast the future, but that their ability to do so depends on the assistance of demons, and that the drawing up of nativities is merely a pretence to cloak this partnership.

Little is known of astronomy as a subject in the Roman schools. It no doubt formed part of the curriculum, but apparently no text-book was produced between the time of Varro and that of Martianus Capella. The three school treatises of late Roman and early medieval times, written by Capella, Cassiodorus, and Isidore, were all the work of educational encyclopedists from whom nothing of a scientific character could be expected.

EXTRACTS

Book III, Chapter 24. On the name of astronomy.

1. Astronomy is the law of the stars, and it traces with inquiring reason the courses of the heavenly bodies, and their figures, and the regular movements of the stars with reference to one another and to the earth.

Chapter 25. On its discoverers.

1. The Egyptians were the first to discover astronomy. And the Chaldeans first taught astrology and the observance of nativity. Moreover, Josephus asserts that Abraham taught astrology to the Egyptians. The Greeks, however, say that this art was first elaborated by Atlas, and therefore it was said that he held the heavens up.

2. Whoever was the discoverer, it was the movement of the heavens and his rational faculty that stirred him, and in the light of the succession of seasons, the observed and established courses of the stars, and the regularity of the intervals, he considered carefully certain dimensions and numbers, and getting a definite and distinct idea of them he wove them into order and discovered astrology.

Chapter 26. On its teachers.

1. In both Greek and Latin there are volumes written on astronomy by different writers. Of these Ptolemy[268] is considered chief among the Greeks. He also taught rules by which the courses of the stars may be discovered.[269]

Chapter 27. The difference between astronomy and astrology.

1. There is some difference between astronomy and astrology. For astronomy embraces the revolution of the heavens, the rise, setting, and motion of the heavenly bodies, and the origin of their names. Astrology, on the other hand, is in part natural, in part superstitious.

2. It is natural astrology when it describes the courses of the sun and the moon and the stars, and the regular succession of the seasons. Superstitious astrology is that which the mathematici follow, who prophesy by the stars, and who distribute the twelve signs of the heavens among the individual parts of the soul or body, and endeavor to predict the nativities and characters of men from the course of the stars.

Chapter 28. On the subject-matter of astronomy.

1. The subject-matter of astronomy is made up of many kinds. For it defines what the universe is, what the heavens, what the position and movement of the sphere, what the axis of the heavens and the poles, what are the climates of the heavens, what the courses of the sun and moon and stars, and so forth.

Chapter 29. On the universe and its name.

1. Mundus (the universe) is that which is made up of the heavens and earth and the sea and all the heavenly bodies. And it is called mundus for the reason that it is always in motion. For no repose is granted to its elements.

Chapter 30. On the form of the universe.

1. The form of the universe is described as follows: as the universe rises toward the region of the north, so it slopes away toward the south; its head and face, as it were, is the east, and its back part the north.

Chapter 31. On the heavens and their name.

1. The philosophers have asserted that the heavens are round, in rapid motion, and made of fire, and that they are called by this name (coelum) because they have the forms of the stars fixed on them, like a dish with figures in relief (coelatum).

2. For God decked them with bright lights, and filled them with the glowing circles of the sun and moon, and adorned them with the glittering images of flashing stars.

Chapter 32. On the situation of the celestial sphere.

1. The sphere of the heavens is rounded and its center is the earth, equally shut in on every side. This sphere, they say, has neither beginning nor end, for the reason that being rounded like a circle it is not easily perceived where it begins or where it ends.

2. The philosophers have brought in the theory of seven heavens of the universe, that is, globes with planets moving harmoniously, and they assert that by their circles all things are bound together, and they think that these, being connected, and, as it were, fitted to one another, move backward and are borne with definite motions in contrary directions.

Chapter 33. On the motion of the same.

1. The sphere revolves on two axes, of which one is the northern, which never sets, and is called Boreas; the other is the southern, which is never seen, and is called Austronotius.

2. On these two poles the sphere of heaven moves, they say, and with its motion the stars fixed in it pass from the east all the way around to the west, the septentriones near the point of rest describing smaller circles.

Chapter 34. On the course of the same sphere.

1. The sphere of heaven, [moving] from the east towards the west, turns once in a day and night, in the space of twenty-four hours, within which the sun completes his swift revolving course over the lands and under the earth.

Chapter 35. On the swiftness of the heavens.

1. With such swiftness is the sphere of heaven said to run, that if the stars did not run against its headlong course in order to delay it, it would destroy the universe.

Chapter 36. On the axis of the heavens.

1. The axis is a straight line north, which passes through the center of the globe of the sphere, and is called axis because the sphere revolves on it like a wheel, or it may be because the Wain is there.

Chapter 37. On the poles of the heavens.

1. The poles are little circles which run on the axis. Of these one is the northern which never sets and is called Boreas; the other is the southern which is never seen, and is called Austronotius.

Chapter 38. On the cardines of the heavens.

1. The cardines of the heavens are the ends of the axis, and are called cardines (hinges) because the heavens turn on them, or because they turn like the heart (cor).

Chapter 40. On the gates of the heavens.

1. There are two gates of the heavens, the east and the west. For by one the sun appears, by the other he retires.

Chapter 42. On the four parts of the heavens.

1. The climata of the heavens, that is, the tracts or parts, are four, of which the first part is the eastern, where some stars rise; the second, the western, where some stars set; the third, the northern, where the sun comes in the longer days; the fourth, the southern, where the sun comes in the time of the longer nights.

4. There are also other climata of the heavens, seven in number, as if seven lines from east to west, under which the manners of men are dissimilar, and animals of different species appear; they are named from certain famous places, of which the first is Meroe; the second, Siene; the third, Catachoras, that is Africa; the fourth, Rhodus; the fifth, Hellespontus; the sixth, Mesopontus; the seventh, Boristhenes.[270]

Chapter 43. On the hemispheres.

1. A hemisphere is half a sphere. The hemisphere above the earth is that part of the heavens the whole of which is seen by us; the hemisphere under the earth is that which cannot be seen as long as it is under the earth.

Chapter 44. On the five circles of the heavens.

1. There are five zones in the heavens, according to the differences of which certain parts of the earth are inhabitable, because of their moderate temperature, and certain parts are uninhabitable because of extremes of heat and cold. And these are called zones or circles for the reason that they exist on the circumference of the sphere.

2. The first of these circles is called the Arctic, because the constellations of the Arcti are visible enclosed within it; the second is called the summer tropic, because in this circle the sun makes summer in northern regions, and does not pass beyond it but immediately returns, and from this it is called tropic.

3. The third circle is called ἰσημερινὸς, which is equivalent to equinoctialis in Latin, for the reason that when the sun comes to this circle it makes equal day and night (for ἰσημερινὸς means in Latin day equal to the night) and by this circle the sphere is seen to be equally divided. The fourth circle is called Antarctic,[271] for the reason that it is opposite to the circle which we call Arctic.

4. The fifth circle is called the winter tropic (χειμερινὸς τροπικός), which in the Latin is hiemalis or brumalis, because when the sun comes to this circle it makes winter for those who are in the north and summer for those who dwell in the parts of the south.

Chapter 47. On the size of the sun.

1. The size of the sun is greater than that of the earth and so from the moment when it rises it appears equally to east and west at the same time.[272] And as to its appearing to us about a cubit in width, it is necessary to reflect how far the sun is from the earth, which distance causes it to seem small to us.

Chapter 48. On the size of the moon.

1. The size of the moon also is said to be less than that of the sun. For since the sun is higher than the moon and still appears to us larger than the moon, if it should approach near to us it would be plainly seen to be much larger than the moon. Just as the sun is larger than the earth, so the earth is in some degree larger than the moon.

Chapter 49. On the nature of the sun.

1. The sun, being made of fire, heats to a whiter glow because of the excessive speed of its circular motion. And its fire, philosophers declare, is fed with water, and it receives the virtue of light and heat from an element opposed to it. Whence we see that it is often wet and dewy.

Chapter 50. On the motion of the sun.

1. They say that the sun has a motion of its own and does not turn with the universe. For if it remained fixed in the heavens all days and nights would be equal, but since we see that it will set to-morrow in a different place from where it set yesterday, it is plain that it has a motion of its own and does not move with the universe. For it accomplishes its yearly orbits by varying courses, on account of the changes of the seasons.

2. For going further to the south it makes winter, in order that the land may be enriched by winter rains and frosts. Approaching the north it restores the summer, in order that fruits may mature, and what is green in the damp weather may ripen in the heat.

Chapter 51. What the sun does.

1. The rising sun brings the day, the setting sun the night; for day is the sun above the earth, night is the sun beneath the earth. From the sun come the hours; from the sun, when it rises, the day; from the sun, too, when it sets, the night; from the sun the months and years are numbered; from the sun come the changes of the seasons.

2. When it runs through the south it is nearer the earth; when it passes toward the north it is raised aloft. God has appointed for it different courses, places, and times for this reason, lest if it always remained in the same place all things should be consumed by its daily heat—just as Clement says: “It takes on different motions, by which the temperature of the air is moderated with a view to the seasons, and a regular order is observed in its seasonal changes and permutations. For when it ascends to the higher parts it tempers the spring, and when it comes to the summit of heaven it kindles the summer heats; descending again, it gives autumn its temperature. And when it returns to the lower circle it leaves to us the rigor of winter cold from the icy quarter of the heavens.”

Chapter 52. On the journey of the sun.

1. The eastern sun holds its way through the south, and after it comes to the west and has bathed itself in ocean, it passes by unknown ways beneath the earth, and again returns to the east.

Chapter 53. On the light of the moon.

1. Certain philosophers hold that the moon has a light of its own, that one part of its globe is bright and another dark, and that turning by degrees it assumes different shapes. Others, on the contrary, assert that the moon has no light of its own, but is illumined by the rays of the sun. And therefore it suffers an eclipse if the shadow of the earth is interposed between itself and the sun.

Chapter 56. On the motion of the moon.

1. The moon governs the times by alternately losing and recovering its light. It advances like the sun in an oblique, and not a vertical course, for this reason, that it may not be opposite the center of the earth and often suffer eclipse. For its orbit is near the earth. The waxing moon has its horns looking east; the waning, west; rightly, because it is going to set and lose its light.

Chapter 57. On the nearness of the moon to the earth.

1. The moon is nearer the earth than is the sun. Therefore having a narrow orbit it finishes its course more quickly. For it traverses in thirty days the journey the sun accomplishes in three hundred and sixty-five. Whence the ancients made the months depend on the moon, the years on the course of the sun.

Chapter 58. On the eclipse of the sun.

1. There is an eclipse of the sun as often as the thirtieth moon reaches the same line where the sun is passing, and, interposing itself, darkens the sun. For we see that the sun is eclipsed when the moon’s orb comes opposite to it.

Chapter 59. On the eclipse of the moon.

1. There is an eclipse of the moon as often as the moon runs into the shadow of the earth. For it is thought to have no light of its own but to be illumined by the sun, whence it suffers eclipse if the shadow of the earth comes between it and the sun. The fifteenth moon suffers this until it passes out from the center and shadow of the interposing earth and sees the sun and is seen by the sun.

Chapter 60. On the distinction between stella, sidus, and astrum.

1. Stellae, sidera, and astra differ from one another. For stella is any separate star. Sidera are made of very many stars, as Hyades, Pleiades. Astra are large stars as Orion, Bootes. But the writers confuse these names, putting astra for stella and stella for sidera.[273]

Chapter 61. On the light of the stars.

1. Stars are said to have no light of their own, but to be lighted by the sun like the moon.

Chapter 62. On the position of the stars.

1. Stars are motionless, and being fixed are carried along by the heavens in perpetual course, and they do not set by day but are obscured by the brilliance of the sun.

Chapter 63. On the courses of the stars.

1. Stars either are borne along or have motion. Those are borne along which are fixed in the heavens and revolve with the heavens. Certain have motion, like the planets, that is, the wandering stars, which go through roaming courses, but with definite limitations.

Chapter 64. On the varying courses of the stars.

1. According as stars are carried on different orbits of the heavenly planets, certain ones rise earlier and set later, and certain rising later come to their setting earlier. Others rise together and do not set at the same time. But all in their own time revolve in a course of their own.

Chapter 65. On the distances of the stars.

1. Stars are at different distances from the earth and therefore, being of unequal brightness, they are more or less plain to the sight; many are larger than the bright ones which we see, but being further away they appear small to us.

Chapter 66. On the circular number of the stars.

1. There is a circular number of the stars by which it is said to be known in what time each and every star finishes its orbit, whether in longitude or latitude.[274]

2. For the moon is said to complete its orbit in eight years, Mercury in twenty, Lucifer in nine, the sun in nineteen, Pyrois in fifteen, Phaeton in twelve, Saturn in thirty. When these are finished, they return to a repetition of their orbits through the same constellations and regions.

3. Certain stars being hindered by the rays of the sun become irregular, either retrograde or stationary, as the poet relates, saying:

Sol tempora dividit aevi

Mutat nocte diem, radiisque potentibus astra

Ire vetat, cursusque vagos statione moratur.

Chapter 67. On the wandering stars.

1. Certain stars are called planetae, that is, wandering, because they hasten around through the whole universe with varying motions....

Chapter 68.

1. Praecedentia or antegradatio of stars is when a star seems to be making its usual course and [really] is somewhat ahead of it.

Chapter 69.

1. Remotio or retrogradatio of stars is when a star, while moving on its regular orbit, seems at the same time to be moving backward.

Chapter 70.

1. The status of stars means that while a star is continuing its proper motion it nevertheless seems in some places to stand still.

Chapter 71. On the names of stars.

3. Stellae is derived from stare, because the stars always remain (stant) fixed in the heavens and do not fall. As to our seeing stars fall, as it were, from heaven, they are not stars but little bits of fire that have fallen from the ether, and this happens when the wind, blowing high, carries along with it fire from the ether, which as it is carried along gives the appearance of falling stars. For stars cannot fall; they are motionless (as has been said above) and are fixed in the heavens and carried around with them.

16. A comet is so-called because it spreads light from itself as if it were hair (comas). And when this kind of star appears it indicates pestilence, famine, or war.

17. Comets are called in the Latin crinitae because they have a trail of flames resembling hair (in modum crinium). The Stoics say there are over thirty of them, and certain astrologers have written down their names and qualities.

20. The planets are stars which are not fixed in the heavens like the rest, but move along in the air.... Sometimes they move towards the south, sometimes towards the north, generally in a direction opposite to that of the universe, sometimes with it, and their Greek names are Phaeton, Phaenon, Pyrois, Hesperus, Stilbon.

21. To these the Romans have given the names of their gods, that is, of Jupiter, Saturn, Mars, Venus, Mercury. Deceiving themselves and wishing to deceive [others] into worship of these gods, who had bestowed upon them somewhat in accordance with the desire of the world, they pointed to the stars in heaven, saying that that was Jove’s star, that Mercury’s, and the empty idea arose. This erroneous belief the devil cherished, but Christ destroyed.

22. Moreover as to the constellations which are given names by the heathen, in which the likeness of living creatures is traced by means of the stars, like Arctos, Aries, Taurus, Libra, and others, they who first discerned constellations in a number of stars were influenced by superstitious vanity and imagined a bodily form, giving them, because of certain reasons, the likenesses and names of their gods.

23. For they named Aries, the first constellation—to which, as to Libra, they assign the middle line of the universe[275]—after Jupiter Ammon, on whose head image makers fix the horns of a ram (arietis cornua).

24. This the heathen set as the first among the constellations because in the month of March, which is the beginning of the year, they say the sun is moving in that constellation.

26. Cancer, too, they so named because when the sun comes to that constellation in the month of June, it begins to move backward in the manner of a crab (in modum cancri), and brings in the shorter days; for in this creature front and rear are indistinguishable and it advances either way, so that its fore part may be behind and its back part before.

32. Moreover Aquarius and Pisces they named from the rainy season, because heavier rains fall in winter when the sun turns at these constellations. And it is a wonderful folly of the heathen that they have raised to the heavens not only fish, but rams also, and he-goats and bulls, she-bears and dogs, crabs and scorpions. They have also placed among the stars of heaven an eagle and a swan, in memory of Jove, because of the myths about him.

33. They believed, too, that Perseus and his wife Andromeda were received into the heavens after their death, so they marked out likenesses of them in the stars, and did not blush to call them by their names.

37. But by whatever fashion of superstition these are named by men, they are nevertheless stars, which God made at the beginning of the universe and ordained to mark the seasons with regular motion.

38. Therefore observations of these constellations, or nativities, or the rest of the superstition that attaches itself to the observance of the stars—that is, to a knowledge of the fates—and is doubtless opposed to our faith, ought to be ignored by Christians in such a way that it would seem they had not been written.

39. But a good many, enticed by the fairness and brightness of the constellations, have in their blindness fallen into the errors of the stars, so that they endeavor to foreknow future events by the noxious computations that are called mathesis; but not only the teachers of the Christian religion, but also Plato and Aristotle and others of the heathen, moved by truth, condemned them with unanimous opinion, saying that confusion as to [future] things was produced rather from such a belief.

40. For if, as they say, men are driven by the compulsion of their birth to various kinds of acts, why should the good deserve praise, or the evil feel the vengeance of the law....

41. This succession of the seven secular disciplines was terminated in astronomy by the philosophers for this purpose forsooth, that it might free souls, entangled by secular wisdom, from earthly matters, and set them at meditation upon the things on high.

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BOOK IV

ON MEDICINE[276]

INTRODUCTION

The Greek science of medicine was one which reached a high degree of development. As early as the fifth century B.C. it appears in the school of Hippocrates, divested of nearly all trace of its origin in superstition and magic, and largely relying on careful observation and interpretation of symptoms. This school already possessed a considerable body of recorded observations. At Alexandria, later, further progress was made, especially in the subject of anatomy. At this time the dissection—and even vivisection—of the human body was practiced, though there are few traces of it earlier, and later it was forbidden. The last great land-mark in the history of ancient medicine is to be found in the works of Galen (second century A.D.) who summed up, extended, and interpreted the medical knowledge of preceding times.

In medicine, however, as in Greek science generally, theoretical and philosophical elements often prevailed to the detriment of the pragmatical. Examples of this are to be seen in the theory of the four humors, first found in the Hippocratic writings; in the belief of the Methodist school, which held that disease consisted in the contraction and relaxation of the pores (πόροι); and in the doctrines of the Pneumatic school, which maintained that health and disease resulted from the influence of the universal soul (πνεῦμα). A reaction against this tendency is evidenced by the empirics, who professed to reject all general notions and to rely on experience alone. However, the increasing predominance of the theoretical is shown in the case of Galen, who secured his ascendency over succeeding ages by his extravagant theoretical system rather than by his really great practical knowledge.

No contribution to medicine was made by the Romans. Although the profession appeared among them in the second century B.C., it remained a thing apart, in the hands of Greek physicians.[277] Of the three chief writers on the subject in the Latin language, two, Celsus and Pliny, were not physicians but encyclopedists, who were necessarily compilers rather than scientists.[278] The only writer of importance who approached his work from a professional standpoint was Caelius Aurelianus, and his book is of importance chiefly because its Greek original is lost.[279] This neglect of medicine is explained in part by the fact that physicians stood low in the social scale. Another more powerful influence was the increasing fashionableness of Oriental religions with their superstition and addiction to magic practices. Toward the close of the empire the decline was rapid in medicine as in other fields. Abridgements, which cut down quality unconsciously as much as they did quantity consciously, held the field. Itinerant quacks and “folk-medicine” gradually ousted the lay profession until finally what little science remained was in the hands of priests and monks, who needed a smattering of the subject for the people of their parishes, and the inmates of monasteries and hospitals.[280]

Isidore does not say for what purpose he wrote his De Medicina, whether to serve as a text-book to aid in the education of the clergy in the way indicated above, or merely in the spirit of the encyclopedist. A number of considerations point strongly to the former conclusion. In the first place, medicine is placed in juxtaposition with the seven liberal arts, and is separated from subjects more nearly akin to it. Secondly, the attitude which Isidore displays in speaking of medicine is one which remembers that this subject was once classed with the liberal arts. He feels called upon to explain why “the art of medicine is not included among the liberal disciplines”, and his explanation is one drawn from the pedagogical sphere; he tells us that medicine is “a second philosophy”, by which he means to say that it belongs to the highest stage of education, but plays therein a minor part. Finally, we must remember that Cassiodorus, whose comprehensive plan of education had great influence with Isidore, had recognized the need of medical knowledge in the education of the clergy, as shown in his chapter “On monks having the care of the infirm”.

It is not known what were the immediate sources of Isidore’s De Medicina. The ultimate authority for his account of diseases is the work of the Methodist Caelius Aurelianus, whose eight books containing a classification of diseases into acute and chronic are reproduced by Isidore in two chapters that occupy the greater part of the space that he devoted to medicine.

EXTRACTS

Chapter 1. On medicine.

1. Medicine is that which guards or restores the health of the body, and its subject-matter deals with diseases and wounds.

2. And so it includes not only those things which are presented in the art (ars) of those who are called medici in the proper sense, but food, drink, and covering as well; in short, all the guarding and defence by which our body is protected against blows and accidents from the outside.

Chapter 2. On its name.

1. Its name is believed to have been given to medicine from modus, that is, moderation, so that not enough but a little be used. For nature is made sorrowful by much and rejoices in the moderate. Whence also they who drink in quantities and without ceasing of herb juices (pigmenta) and antidotes, are troubled. For all immoderation brings not welfare but danger.

Chapter 3. On the founders of medicine.

1. Apollo is called among the Greeks the author and founder of the art of medicine. His son, Aesculapius, enlarged it by his fame and work. But after Aesculapius perished by a thunder-bolt, the business of curing is said to have been forbidden and the art disappeared with its author.

2. And it remained unknown for nearly five hundred years down to the time of Artaxerxes, king of the Persians. Then Hippocrates, born in the island of Cos, his father being Asclepius, brought it back to the light of day.

Chapter 4. On the three schools (haereses) of medicine.

1. And so these three men founded as many schools. The first, Methodica,[281] was established by Apollo, and it follows remedies and charms. The second, Empirica,[282] that is, relying on experience, was established by Aesculapius, which depends not on the interpretation of symptoms, but on experience alone. The third, Logica,[283] that is, rational, was invented by Hippocrates.

2. For the latter, separating the qualities of ages, districts, and diseases, examined the practice of the art in a rational way. The Empirici, then, follow experience alone; the Logici add reason to experience; the Methodici observe neither the elements, nor seasons, nor ages, nor causes, but the substances of diseases alone.

Chapter 5. On the four humors of the body.

1. Health is the integrity of the body and the compound (temperantia) made by nature from hot and moist which is the blood, whence also it has been named sanitas, as it were sanguinis status (state of the blood).

2. Under the general name of morbus (disease) all disorders of the body are embraced, to which the ancients gave the name of morbus in order to indicate by the very name the power of death (mortis) which arises from it. Between health and disease the mean is cure, and unless it harmonizes with the disease it does not lead to health.

3. All diseases arise from the four humors, that is, from blood, bile, black bile, and phlegm. Just as there are four elements so also there are four humors, and each humor imitates its element: blood, air; bile, fire; black bile, earth; phlegm, water. There are four humors, as four elements, which preserve our bodies.

4. Sanguis[284] (blood) took its name from a Greek source, because it invigorates, sustains and gives life to the body. Cholera[285] (bile) the Greeks named because it is ended in the space of one day, whence it was named cholera, that is, fellicula, that is, effusion of bile (fel). For the Greeks call bile χολή.

5. Melancholia (black bile) is named because an abundance of bile has been mixed with the dregs of black blood....

6. Sanguis in the Latin is so-called because it is suavis, whence men in whom sanguis is predominant are pleasant and bland.

7. Phlegma they have named because it is cold. For the Greeks call cold φλέγμονα. According to these four humors the well are governed, and from them the diseases of the infirm arise. For when they have grown too great beyond the course of nature, they cause illnesses.

8. From blood and bile acute disorders come, which the Greeks call ὀξέα; from phlegm and black bile troubles of long standing, which the Greeks call χρόνια.

Chapter 6. On acute diseases.

1. Oxea is acute disease which either quickly passes or more quickly kills, as pleurisy, phrensy, for ὀξὺ in Greek means swift and sharp. χρόνια is prolonged bodily disease which lingers through many seasons, as gout, phthisis.... Certain disorders have received their names from causes proper to them.

2. Febris (fever) is derived from fervor, for it is an excess of heat.

3. Frenzy is so-called because the mind is affected, since the Greeks call the mind φρένες, or else because they gnash (infrendant) with the teeth, for frendere means to strike the teeth together. It is excitement with exasperation and dementia caused by the power of bile.

17. Pestilence is a contagion, and when it seizes one it quickly passes to more. It is produced from a corruption of the air, and makes its way by penetrating into the inward parts. Although this is generally caused by the powers of the air, still it is certainly not caused against the will of Omnipotent God.... It is a disease so acute that it affords no time to hope for life or death, but a sudden weakness and death come at the same moment.

Chapter 7. On chronic diseases.

3. Scotoma took its name from an accidental quality, because it brings a sudden darkness to the eyes along with a whirling (vertigo) of the head. Now there is a whirling as often as the wind rises and starts the dust going round and round.

4. So too in man’s head the air passages[286] and the veins produce a windiness from the resolving of moisture[287] and make a whirling in his eyes whence vertigo is named.

5. Epilepsy took its name because while seizing the mind it also holds the body. For the Greeks call seizure ἐπιληψία. And it comes from the melancholy humor whenever it becomes abundant and has turned toward the head. This disorder is also called caduca (the falling sickness), because the sick man falls and suffers from spasms.

6. The common herd call these also lunatici because their madness[288] comes upon them according to the course of the moon....

Chapter 8. On diseases that appear on the surface of the body.

11. Leprosy is a scaly roughness of the skin, like lepidus (pepper-wort), whence it took its name, and its color now turns to black, now to white, now to red. On the body of a man leprosy is diagnosed in this way, if a varied color appears here and there between sound parts of the skin, or if it spreads everywhere in such a way as to make all of one unnatural color.

12. The morbus elephantiacus[289] is so called from the resemblance to an elephant, whose naturally hard and rough skin gave the name to the disease among men, because it makes the surface of the body like the hide of an elephant; or it may be because it is a great disorder, like the animal itself from which it has derived its name.

Chapter 9. On remedies and medicines.

1. The curative power of medicine must not be despised. For we remember that Isaiah sent something of medicinal nature to Hezekiah when he was sick, and Paul the apostle said a little wine was good for Timothy.

3. There are three kinds of cures in all. The first is the dietetic; the second, the pharmaceutical; the third, the surgical. Diet (diaeta) is the observance of the law of life. Pharmacy is curing by medicines. Surgery is cutting with the knife; for with the knife is cut away that which does not feel the healing of medicines....

5. Every cure is wrought either by contraries or by likes. By contraries, as cold by warm and dry by moist, just as in man pride cannot be cured except by humility.

6. By likes, as a round bandage is put on a round wound, or an oblong one on an oblong wound. For the very bandage is not the same for all wounds, but like is fitted to like....

7. Antidotum in the Greek means in the Latin ex contrario datum. For contraries are cured by contraries in the medical system. On the other hand likes are cured by likes, as for example, πικρὰ which means bitters because its taste is bitter. It received a suitable name because the bitterness of disease is dispelled by its bitterness.

Chapter 13. On the beginning of medicine.[290]

1. Inquiry is made by certain why the art of medicine is not included among the liberal disciplines. Because of this, that they embrace separate subjects, but medicine embraces all. For the physician is commanded to know grammar, in order to be able to understand and set forth what he reads.

2. In like manner rhetoric, too, that he may be able to define by true arguments the diseases which he treats. Moreover logic, to scrutinize and cure the causes of infirmities by the aid of reason. So, too, arithmetic, on account of the number of hours in paroxysms and of the days in periods.

3. In the same manner geometry, on account of the qualities of districts and the situations of places, in respect to which it teaches what one ought to observe. Moreover, music will not be unknown to him, for there are many things that are read of as accomplished by this discipline in the case of sick men, as it is read of David that he saved Saul from an unclean spirit by the art of melody. The physician Asclepiades, too, restored one who was subject to frenzy to his former health by music.

4. Lastly, he will know astronomy, by which to contemplate the system of the stars and the change of the seasons, for as a certain physician says, our bodies change too, along with the qualities of the heavens. Hence it is that medicine is called “a second philosophy”. For both disciplines claim the whole man. For as by one the soul is cured, so is the body by the other.

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