[495] Bouterwek, ix. 332-354, v. 113. Heinsius, iv. 113. Warton, iii. 74.
Historical works.
Ph. de Comines. 134. The historical literature of this century presents very little deserving of notice. The English writers of this class are absolutely contemptible; and if some annalists of good sense and tolerable skill in narration may be found on the Continent, they are not conspicuous enough to arrest our regard in a work which designedly passes over that department of literature, so far as it is merely conversant with particular events. But the memoirs of Philip de Comines, which, though not published till 1529, must have been written before the close of the fifteenth century, are not only of a higher value, but almost make an epoch in historical literature. If Froissart, by his picturesque descriptions, and fertility of historical invention, may be reckoned the Livy of France, she had her Tacitus in Philip de Comines. The intermediate writers, Monstrelet and his continuators, have the merits of neither, certainly not of Comines. He is the first modern writer, (or, if there had been any approach to an exception among the Italians, it has escaped my recollection,) who in any degree has displayed sagacity in reasoning on the characters of men, and the consequences of their actions, or who has been able to generalise his observation by comparison and reflection. Nothing of this could have been found in the cloister; nor were the philologers of Italy equal to a task which required capacities and pursuits very different from their own. An acute understanding and much experience of mankind gave Comines this superiority; his life had not been spent over books; and he is consequently free from that pedantic application of history, which became common with those who passed for political reasoners in the next two centuries. Yet he was not ignorant of former times; and we see the advantage of those translations from antiquity, made during the last hundred years in France, by the use to which he turned them.
Algebra. 135. The earliest printed treatise of algebra, for that of Leonard Fibonacci is still in manuscript, was published in 1494, by Luca Pacioli di Borgo, a Franciscan, who taught mathematics in the university of Milan. This book is written in Italian, with a mixture of the Venetian dialect, and with many Latin words. In the first part, he explains the rules of commercial arithmetic in detail, and is the earliest Italian writer who shows the principles of Italian book-keeping by double entry. Algebra he calls l’arte maggiore, detta dal volgo la regola de la cosa, over alghebra e almacabala, which last he explains by restauratio et opposito. The known number is called no or numero; co. or cosa stands for the unknown quantity; whence algebra was sometimes called the cossic art. In the early Latin treatises Res is used, or R., which is an approach to literal expression. The square is called censo or ce.; the cube, cubo or cu.; p. and m. stand for plus and minus. Thus, 3co. p. 4ce. m. 5cu. p. 2ce. ce. m. 6no would have been written for what would now be expressed 3x + 4x2 - 5x3 + 2x4 - 6. Luca di Borgo’s algebra goes as far as quadratic equations; but though he had very good notions on the subject, it does not appear that he carried the science much beyond the point where Leonard Fibonacci had left it three centuries before. And its principles were already familiar to mathematicians; for Regiomontanus, having stated a trigonometrical solution in the form of a quadratic equation, adds, quod restat, præcepta artis edocebunt. Luca di Borgo perceived, in a certain sense, the application of algebra to geometry, observing, that the rules as to surd roots are referrible to incommensurable magnitudes.[496]
[496] Montucla. Kästner. Cossali. Hutton’s Mathem. Dict., art. Algebra. The last writer, and perhaps the first, had never seen the book of Luca Pacioli.
Mr. Colebrooke, in his Indian Algebra, has shown that the Hindoos carried that science considerably farther than either the Greeks or the Arabians (though he thinks they may probably have derived their notions of the science from the former), anticipating some of the discoveries of the sixteenth century.
Events from 1490 to 1500. 136. This period of ten years from 1490 to 1500, will ever be memorable in the history of mankind. It is here that we usually close the long interval between the Roman world and this our modern Europe, denominated the Middle Ages. The conquest of Granada, which rendered Spain a Christian kingdom; the annexation of the last great fief of the French crown, Britany, which made France an entire and absolute monarchy; the public peace of Germany; the invasion of Naples by Charles VIII., which revealed the weakness of Italy, while it communicated her arts and manners to the cisalpine nations, and opened the scene of warfare and alliances which may be deduced to the present day; the discovery of two worlds by Columbus and Vasco de Gama, all belong to this decade. But it is not, as we have seen, so marked an era in the progression of literature.
Close of fifteenth century. 137. In taking leave of the fifteenth century, to which we have been used to attach many associations of reverence, and during which the desire of knowledge was, in one part of Europe, more enthusiastic and universal than perhaps it has since ever been, it is natural to ask ourselves what harvest had already rewarded their zeal and labour, what monuments of genius and erudition still receive the homage of mankind?
Its literature nearly neglected. 138. No very triumphant answer can be given to this interrogation. Of the books then written how few are read! Of the men then famous how few are familiar in our recollection! Let us consider what Italy itself produced of any effective tendency to enlarge the boundaries of knowledge, or to delight the taste and fancy. The treatise of Valla on Latin grammar, the miscellaneous observations of Politian on ancient authors, the commentaries of Landino and some other editors, the Platonic theology of Ficinus, the Latin poetry of Politian and Pontanus, the light Italian poetry of the same Politian and Lorenzo de’ Medici, the epic romances of Pulci and Boiardo. Of these, Pulci alone, in an original shape, is still read in Italy, and by some lovers of that literature in other countries, and the Latin poets by a smaller number. If we look on the other side of the Alps, the catalogue is much shorter, or rather does not contain a single book, except Philip de Comines, that enters into the usual studies of a literary man. Froissart hardly belongs to the fifteenth century, his history terminating about 1400. The first undated edition, with a continuation by some one to 1498, was printed between that time and 1509, when the second appeared.