FOOTNOTES:
[115] Histoire des Mathématiques, vol. i. p. 97.
[116] De vi Percussionis, Bononiæ, 1667.
[117] Mec. Analyt.
[118] Mechanica.
[119] Diog. Laert. In vit. Archyt.
[120] De Cœlo, lib. i. c. 1.
[121] Phys. lib. i. c. 3.
[122] Lib. iii. c. 2. The Aristotelians distinguished between things as existing in act or energy (ενεργεια) and things in capacity or power (δυναμις). For the advantage of those who may think the distinction worth attending to, we give an illustration of Aristotle's meaning, from a very acute and learned commentator:—"It (motion) is something more than dead capacity; something less than perfect actuality; capacity roused, and striving to quit its latent character; not the capable brass, nor yet the actual statue, but the capacity in energy; that is to say, the brass in fusion while it is becoming the statue and is not yet become."—"The bow moves not because it may be bent, nor because it is bent; but the motion lies between; lies in an imperfect and obscure union of the two together; is the actuality (if I may so say) even of capacity itself: imperfect and obscure, because such is capacity to which it belongs."—Harris, Philosophical Arrangements.
[123] Lib. iv. c. 1.
[124] Lib. iv. c. 11.
[125] De Cœlo, lib. i. c. 2.
[126] Phys. lib. vii. c. 8.
[127] De Cœlo, lib. i. c. 6.
[128] Phys. lib. vii. c. 2.
[129] Mechanica.
[130] Εαν δε εν μηδενι λογῳ φερηται δυο φορας κατα μηδενα χρονον, αδυνατον ευθειαν ειναι την φοραν. Εαν γαρ τινα λογον ενεχθῃ εν χρονῳ τινι τουτον αναγκη τον χρονον ευθειαν ειναι φοραν δια τα προειρημενα, ὡστε περιφερες γινεται δυο φερομενον φορας εν μηδενι λογῳ μηδενα χρονον.—i.e. v = ds/ dt
[131] De Cœlo, lib. i. c. 3.
[132] Lib. iv. c. 2.
[133] Phys., lib. iv. c. 8.
[134] De Proport. Basileæ, 1570.
"Nunc locus est, ut opinor, in his illud quoque rebus
Confirmare tibi, nullam rem posse suâ vi
Corpoream sursum ferri, sursumque meare.—
Nec quom subsiliunt ignes ad tecta domorum,
Et celeri flammâ degustant tigna trabeisque
Sponte suâ facere id sine vi subicente putandum est.
—Nonne vides etiam quantâ vi tigna trabeisque
Respuat humor aquæ? Nam quod magi' mersimus altum
Directâ et magnâ vi multi pressimus ægre:—
Tam cupide sursum revomit magis atque remittit
Plus ut parte foras emergant, exsiliantque:
—Nec tamen hæc, quantu'st in sedubitamus, opinor,
Quinvacuum per inane deorsum cuncta ferantur,
Sic igitur debent flammæ quoque posse per auras
Aeris expressæ sursum subsidere, quamquam
Pondera quantum in se est deorsum deducere pugnent.
—Quod si forte aliquis credit Graviora potesse
Corpora, quo citius rectum per Inane feruntur,
—Avius a verâ longe ratione recedit.
Nam per Aquas quæcunque cadunt atque Aera deorsum
Hæc pro ponderibus casus celerare necesse 'st
Propterea quia corpus Aquæ, naturaque tenuis
Aeris haud possunt æque rem quamque morari:
Sed citius cedunt Gravioribus exsuperata.
At contra nulli de nullâ parte, neque ullo
Tempore Inane potest Vacuum subsistere reii
Quin, sua quod natura petit, considere pergat:
Omnia quâ propter debent per Inane quietum
Æque ponderibus non æquis concita ferri."
De Rerum Natura, lib. ii, v. 184-239.
[ [136] Math. Coll. Pisani, 1662.
[137] Œuvres Mathématiques. Leyde, 1634.
[138] This is not a literal translation, but by what follows, is evidently the Author's meaning. His words are, "Proportionem igitur declinationum dico non angulorum, sed linearum usque ad æquidistantem resecationem in quâ æqualiter sumunt de directo."
[139] Opusculum De Ponderositate. Venetiis, 1565.