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Lect.VIII. Mathematical Lectures. i2£
pies is only ufed by Euclid in his first Book, m
the following Books it is contemned : Contemned is
it, how does that appear ? Certainly he elfewhere
ufes other Definitions and other Axioms as occafion
requires •, it is true he adds no more Poftulates,
becaufe there feems to be no need of more: But
where does he confound thofe Species of Principles,
or declare his Contempt of any of them ? Unlefs
not unfeafonably to name them be to contemn
them.
But perhaps he will object the moft weighty
Authority of Archimedes, who promifcuoufly calls
the Principles laid down before his Iforrhopics
lulates. or Things required. We require it as
a Populate* fiys he, that equal Weights hanging by
equal Lengths do weigh equally* or are in ALquilibrio.
And after the fame manner does Euclid in his Optics call all the Principles he affumes Hypothefes :
Geminus with Proclus* and Eutocius did once make
the fame Obfervation concerning Archimedes : To
which Inftance I anfwer, that perhaps Archimedes Studying Brevity, and not willing to make too great an
Apparatus to a fmall Book, did on purpofe neglect that extreme Exactnefs, which he obferved
his Books of the Sphere and Cylinder* of Spiral
Lines* and other more curious Pieces, where he fe-
parates Definitions from Axioms. Nor is it any
wonder for the fame Words to be fometimes more,
and fometimes lefs extenfive, according to the
Defign and Purpofe of the Writer. Like as the
Stoics* thofe famous Reformers of Things, as well
as Words, do give univerfal Propofitions the
Title of Axioms*. as if they meant to make all
Propofitions equal in Dignity, as they have done
of Virtues and Vices. Nor do I deny but the
word Poftulate, or Petition, from its vulgar Signification, may be fitly enough attributed to all kinds
of Principles. For a Teacher mult in Part petition
| Title | Usefulness of mathematical learning explained and demonstrated. |
| Alternative Title | The usefulness of mathematical learning explained and demonstrated, being mathematical lectures read in the publick schools at the University of Cambridge, by Isaac Barrow... To which is prefixed the oratorical preface of our learned author, spoke before the university on his being elected Lucasian professor of mathematics. Tr. by the Revd. Mr. John Kirkby. |
| Reference Title | Barrow, Isaac, 1734, Usefulness of mathematical learning. |
| Creator | Barrow, Isaac, 1630-1677 |
| Subject | Mathematics -- Philosophy |
| Publisher | London, S. Austen. |
| DateOriginal | 1734 |
| Format | JP2 |
| Extent | 31 cm. |
| Identifier | 1135 |
| Call Number | QA7.B3 1734 |
| Language | English |
| Collection | History of Mathematics |
| Rights | http://www.lindahall.org/imagerepro/ |
| Data contributor | Linda Hall Library, LHL Digital Collections. |
| Type | Image |
| Title | Page 125. |
| Format | tiff |
| Identifier | 1135_163 |
| Relation-Is part of | Is part of : The usefulness of mathematical learning explained and demonstrated, being mathematical lectures read in the publick schools at the University of Cambridge, by Isaac Barrow... To which is prefixed the oratorical preface of our learned author, spoke before the university on his being elected Lucasian professor of mathematics. Tr. by the Revd. Mr. John Kirkby. |
| Rights | http://www.lindahall.org/imagerepro/ |
| Type | Image |
| OCR transcript | Lect.VIII. Mathematical Lectures. i2£ pies is only ufed by Euclid in his first Book, m the following Books it is contemned : Contemned is it, how does that appear ? Certainly he elfewhere ufes other Definitions and other Axioms as occafion requires •, it is true he adds no more Poftulates, becaufe there feems to be no need of more: But where does he confound thofe Species of Principles, or declare his Contempt of any of them ? Unlefs not unfeafonably to name them be to contemn them. But perhaps he will object the moft weighty Authority of Archimedes, who promifcuoufly calls the Principles laid down before his Iforrhopics lulates. or Things required. We require it as a Populate* fiys he, that equal Weights hanging by equal Lengths do weigh equally* or are in ALquilibrio. And after the fame manner does Euclid in his Optics call all the Principles he affumes Hypothefes : Geminus with Proclus* and Eutocius did once make the fame Obfervation concerning Archimedes : To which Inftance I anfwer, that perhaps Archimedes Studying Brevity, and not willing to make too great an Apparatus to a fmall Book, did on purpofe neglect that extreme Exactnefs, which he obferved his Books of the Sphere and Cylinder* of Spiral Lines* and other more curious Pieces, where he fe- parates Definitions from Axioms. Nor is it any wonder for the fame Words to be fometimes more, and fometimes lefs extenfive, according to the Defign and Purpofe of the Writer. Like as the Stoics* thofe famous Reformers of Things, as well as Words, do give univerfal Propofitions the Title of Axioms*. as if they meant to make all Propofitions equal in Dignity, as they have done of Virtues and Vices. Nor do I deny but the word Poftulate, or Petition, from its vulgar Signification, may be fitly enough attributed to all kinds of Principles. For a Teacher mult in Part petition |
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