The history of philosophy, in eight parts by Thomas Stanley.

CHAP. VII.

His Inventions.

HE added much to learning and language by many inventi∣ons, as well of things as of words. To omit Dialectick, of which we treated last,a 1.1 Phavorinus attributes to his invention, discoursing by way of Question; but Aristotle ascribes it to Alexame∣nus, a Styrian or Teian, and it appears by the Dialogues of Plato, that Socrates also used that form of arguing. Laertius informes us, that Zeno Ele••tes was the first composer of Dialogues; yet in my opinion, saith he, Pla••o hath so much refined the form thereof, that he deserves to be preferr'd before all others, as well for invention as reformation.

More properly may be attributed to him the invention ofb 1.2 Ana∣lyticall Method, which reduceth the thing sought unto its principle, the best of Methods. He taught it to Leodamas, and by it found out ma∣ny things in Geometry: Analysis, as defined by thec 1.3 Scholiast up∣on Euclid, is a sumption of the thing sought, by the consequents, (as if it were already known) to find out the truth. Examples thereof we find in the five first propositions of the 13^t• Book of Euclid, besides se∣verall others, that occurre in Apollonius Pergaeus, and Pappus Alexandrinus.

Amongst his Geometricall Inventions also must be remembred the duplication of a Cube, the occasion and manner whereof is rela∣ted byd 1.4 Plutarch ande 1.5 Philoponus. The Delians afflicted with the Pestilence, consulted the Oracle of Apollo; he answer'd, the Plague would cease if they doubled their•• Altar, which was of a Cubick figure. Plu••arch saith, that hereupon the Overseers of the Altar made all the four sides double to what they were before, & so in∣stead of doubling the Altar, they made it octuple to what it was. Philoponus saith, they caused another Cube of the same bignesse with the former to be set upon it, whereby they changed the fi∣gure of the Altar, which was no longer a Cube, but 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, a qua∣drilaterall Pillar. The first way, it was Cubicall, but not double, the second way double, but not Cubicall. The Plague not cea∣sing, they consulted the Oracle again. Apollo answer'd, they had not fulfilled his Command, which was to build a Cubicall Al∣tar as big again as the former. Hereupon they went to Plato, as most skilfull in Geometry, to learn of him the Oracle's meaning, and how they should find out the way of doubling a Cube, re∣taining the Cubick figure. Plato answered, that the God mocked the Grecians for their neglect of Philosophy and Learning, in∣sulting over their ignorance, that he commanded them seri∣ously, to addict themselves to Geometry, that this could not be done any other way, then by finding out two mean proportio∣nalls between two right lines in a Duple proportion (Plato's par∣ticular

method herein is delivered, Eutocius in his comment upon the first proposition of the second Book of Archimedes de Sphaera & Cylindro.) He added that Eudoxus the Gnidian, or Helico the Ci∣zycene would do it for them, That the God needed not this dupli∣cation of his Altar, but commanded all the Grceians, that avoy∣ding war and the miseries wherewith it is attended, they should apply themselves to the Muses; and having setled the turbulent commotions of their minds, converse harmlessly and beneficially with one another. Philoponus addes, that Plato expounded this Pro∣blem to his Disciples, who writ much upon this subject, though nothing thereof be extant. Of the Antients, labour'd in this Problem be∣sides Plato, Archytas the Tarentine, Menaechmus, Eratosthenes, Philo of Byzantium, Hero, Apollonius Pergaeus; Nicomedes, Diocles and Spo∣rus. f 1.6 Valerius Maximus saith, that Plato remitted the Overseers of the sacred Altar to Euclid the Geometrician, as submitting to his Science and Profession; but this is an Errour, because Euclid the Geome∣trician was much later then Plato, and the other Euclid, Plato's contemporary, nothing eminent in Mathematicks, as hath been before me observed byg 1.7 Sir Henry Savile.

That Plato invented many other things in the Mathematicks, (more then appears from those writings of his that are extant) and was most eminent therein, may be argued from the three Books of Theon Smyrnaeus, the first Arithmetick, the second Harmo∣nicks, the last, (not yet publish'd) Astronomy. Those Books contain∣ed many things, singular and choice, not to be met elsewhere. The design is acknowledg'd by the Author, to be as an introduction necessary to the understanding of Plato's writings.

There are also divers words of which he is esteemed to be the first Author, ash 1.8 Antipodes, a word by him first introduced into Philosophy, to signifie those people whose feet are diametrically opposite.

i 1.9 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, Element, untill his time was confounded with 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, Principle, by all Philosophers from Thales. Plato distinguish'd them thus, 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, principle is that which hath nothing before it whereof it might be generated; 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, Elements are com∣pounded.

k 1.10 The word Poem also, though since very triviall, was not u∣sed by any before him.

l 1.11 He first used this term, 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, oblong number, [in Theaeteto] thereby signifying the product of a greater number multiplyed by a lesser.

m 1.12 He also first introduced the word 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, Superficies, for which before was used 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉 a Plane. Thus Laertius, though n 1.13 Proclus implies, that neither Plato nor Aristotle use the word, but for it 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉. Divine Plato, saith he, calls Geometry the Contem∣platrix of Planes, opposing it to Stereometry, as if Plane and Superficies w••re the same. So likewise doth Aristotle. But Euclid and those who

succeed him, make Superficies the genus, plane a species thereof.

o 1.14 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, Divine Providence, a word since much used by Christians, was first the expression of Plato.

p 1.15 He first of Philosophers wrote against Lysias, Son of Cephaluo, in Phaedro.

q 1.16 He first considered the force and efficacy of Grammar.

r 1.17 He first wrote against all that were before him, whence it is wondred at that he never mentions Democritus.

Notes

• a 1.1

  L••••rt.
• b 1.2

  Laert. Procl. in Euclid. lib. 3.
• c 1.3

  Lib. 13.
• d 1.4

  de 〈◊〉〈◊〉 delph.
• e 1.5

  In Anal. post. lib. 1. cap. 7.
• f 1.6

  8. 13.
• g 1.7

  Praele••. 1.
• h 1.8

  Laert.
• i 1.9

  Laert.
• k 1.10

  Laert.
• l 1.11

  Laert.
• m 1.12

  Laert.
• n 1.13

  In Euclid. lib. 2.
• o 1.14

  Laert.
• p 1.15

  Laert.
• q 1.16

  Laert.
• r 1.17

  Laert.