The Usefullness of Mathematical Learning

Explained and Demonstrated

Isaac Barrow

• Publisher: Routledge
• Year: 2013
• eBook ISBN:
  9781317845539
• Topic: Pedagogía
• Subtopic: Educación general

This is a collection of mathematical lectures that were read in the Publick Schools at the University of Cambridge and was originally published in 1734. It includes twenty-three lectures which range in topic from the name and general division of mathematical sciences, to An answer to Borellus' Objections.

An Alphabetical

INDEX

OF THE

Principal Matters

Contained in this Work.

A.

ABstraction, what, Pages 10, 11. Common to all Sciences, 13.

Acoustics, what, 24.

Action, inconceivable without Motion, 173.

Adspective, what, 17.

Affections of Magnitude, common and proper, 84. Of equal Order, 86, 134. May be reciprocally deduced from each other, 86. Some more simple than others, 87. General Affections, 139, &c.

Affections of natural Things, not demonstrable, 62,

Algebra, what, 28.

Algebraical Powers capable of being exhibited geometrically, 44.

Altimetry, what, 51, 265.

Analogy, Signification of the Word, 385, 386. See Proportionality.

Analysis, what, 28.

Apollonius, unjustly blamed by Proclus, 60, 78, 229.

Archimedes, his sparing Assumption of Principles, 59. Calls all his Principles Postulates, 125. His Epitagmata, 127.

Aristides, his Diftinction of arithmetical Reason from geometrical, 343, His Definition of the Genus of Music, 348.

Aristotle, his Acceptation of the Term Mathematics, 2. His improper Use of

10, His Distribution of the Mathematics, 15. Inconsistent with himself, 118. His Definition of Infinite, 142. Confounds Space with Magnitude, 164. Thought Equality needed not to be defined, 198. His Rule of judging, 207, 239. His Axiom concerning the Proportion of Finite and Infinite, 297. His Definitions of Relatives, 332. A false Principle in his Topics, 418.

Arithmetic, what, 11. The same with Geometry, 29, &c.

Astrology, (or Astronomy,) what, 18, 23.

Asymmetry. See Incommensurability.

Asymptotical Lines demonstrate the infinite Divisibility of Magnitude, 155.

St. Austine, his Saying concerning Time, 139.

Automato-poetics, what, 18.

Axioms matbematical univerfally true, 56. None simply indemonstrable, 103, 229, 232. Ought to be demonstrated, if need be, 104, 200. How demonstrable, 105, 228. Need not appear necessarily true, 105, 106. See Principles.

B.

Balisticks, what, 26.

Belopoetics, what, 26.

J. Benedictus, his Mistake about Proportionals, 428.

Blancanus, his Distribution of the Mathematics, 20.

Judged mathematical Figures to have no Existence, but in the Mind, 76.

Borellus, his Agreement wi...

Table of contents

• Cover
• Title Page
• Copyright Page
• Table of Contents
• LECTURE I. OF the Name and General Division of the Mathematical Sciences
• LECTURE II. Of the particular Division of the Mathematical Sciences
• LECTURE III. Of the Identity of Arithmetic and Geometry
• LECTURE IV. Of the Unfitness of the common Division of Mathematics into Speculative and Practical, and of the Excellence of Mathematical Demonstration
• LECTURE V. Containing Answers to the Objections which are usually brought against Mathematical Demonstration
• LECTURE VI. Of the Causality of Mathematical Demonstration
• LECTURE VII. Of the Nature of First Principles
• LECTURE VIII. Of the Division of First Principles
• LECTURE IX. Of the Termination, Extension, Composition, and Divisibility of Magnitudes
• LECTURE X. Of Space and Impenetrability
• LECTURE XI. Of the Congruity and Equality of Magnitudes
• LECTURE XII. An Examination of the Objections brought by Proclus &c.
• LECTURE XIII. Of the erroneous Comment of Proclus and others on the eighth Axiom of the first Element &c.
• LECTURE XIV. Of the different Acceptations of the Word Measure
• LECTURE XV. Of the Acceptation of the Word paronymous to Measure, viz. Mensurability, Mensuration, Commensurability, and Incommensurability
• LECTURE XVI. Of the Homogeneity and Heterogeneity of Quantities
• LECTURE XVII. Of the Names and Diversities of the twofold Kind of Reason or Proportion, viz. Arithmetical and Geometrical
• LECTURE XVIII. A Defence of Euclid’s Definition of Reason or Proportion
• LECTURE XIX. Of the Species and Differences of Geometrical Reason
• LECTURE XX. That Reason are not Quantities
• LECTURE XXI. A Defence of Euclid’s Definition of Proportionals in his fifth Book.
• LECTURE XXII. An Answer to the Objectious against Euclid’s Definition of Proportionals
• LECTURE XXIII. An Answer to Borellus’s Objections, and of the Insufficiency of the Definitions of Proportionality which are substituted in the Room of Euclid’s
• Index