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Lect. VIII. Mathematical Lectures. 123
fions of the Matter ? So that I can't fee what led
the Philofopher to this Distinction, nor does his
Interpreters remove the Scruple.
As to what is faid by Proclus (for firft of all
I aim at him) while he profeffes to follow Ariftotle,
he, in my opinion, renders all things worfe. For
ift. He attributes three kinds of Principles to
Euclid, viz. Axioms* Hypothefies, and Populates,
whofe Differences he expounds according to the
Sentiment of Ariftotle : But as if Definitions were not
Principles, nor did either Euclid or Ariftotle ever
account them for Principles, nor did the latter molt
exprefly diftinguifh them from Hypotheses. Therefore the Blindnefs of Proclus feems wonderful,
both in wholly omitting Definitions in his Enumeration of Principlei, and in confounding them with
the Hypothefes of Ariftotle ; while he very incongruously attributes thofe Things to the Definitions
and Poftulates of Euclid, which Ariftotle afcribes to
his demonftrable Hypothefes and Poftulates. For
how are Euclid's Definitions and Geometrical
Poftulates demonftrable ? How is it neceffary for
the Sentiment of a Learner to be oppofite to the
Poftulates of Euclid ? Or how can that be truly
adapted to them, that however a Learner refufie his
Affent, yet he is admitted a Hearer whether he will
or no ? What is this elfe but to overturn the Foundation of Geometry, and destroy all Learning at
once ? Whereas the Poftulates of Euclid do carry
fo clear a Poffibility, and snay be illuftrated with
fo many familiar Examples, that no Genius capable of Science can any way impugn, or find
Fault with them : Nay, otherwife a Teacher would
become immodeft, importunate and trifling, who
fhould require or fuppofe it •, and in vain would go
about to teach or demonftrate, his Poftulates being
not admitted. But why do I oppofe Proclus,
when he oppofes himfelf, and feems to remove
thofe
| 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 123. |
| Format | tiff |
| Identifier | 1135_161 |
| 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. 123 fions of the Matter ? So that I can't fee what led the Philofopher to this Distinction, nor does his Interpreters remove the Scruple. As to what is faid by Proclus (for firft of all I aim at him) while he profeffes to follow Ariftotle, he, in my opinion, renders all things worfe. For ift. He attributes three kinds of Principles to Euclid, viz. Axioms* Hypothefies, and Populates, whofe Differences he expounds according to the Sentiment of Ariftotle : But as if Definitions were not Principles, nor did either Euclid or Ariftotle ever account them for Principles, nor did the latter molt exprefly diftinguifh them from Hypotheses. Therefore the Blindnefs of Proclus feems wonderful, both in wholly omitting Definitions in his Enumeration of Principlei, and in confounding them with the Hypothefes of Ariftotle ; while he very incongruously attributes thofe Things to the Definitions and Poftulates of Euclid, which Ariftotle afcribes to his demonftrable Hypothefes and Poftulates. For how are Euclid's Definitions and Geometrical Poftulates demonftrable ? How is it neceffary for the Sentiment of a Learner to be oppofite to the Poftulates of Euclid ? Or how can that be truly adapted to them, that however a Learner refufie his Affent, yet he is admitted a Hearer whether he will or no ? What is this elfe but to overturn the Foundation of Geometry, and destroy all Learning at once ? Whereas the Poftulates of Euclid do carry fo clear a Poffibility, and snay be illuftrated with fo many familiar Examples, that no Genius capable of Science can any way impugn, or find Fault with them : Nay, otherwife a Teacher would become immodeft, importunate and trifling, who fhould require or fuppofe it •, and in vain would go about to teach or demonftrate, his Poftulates being not admitted. But why do I oppofe Proclus, when he oppofes himfelf, and feems to remove thofe |
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