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Lect. XXII. Mathematical Lectures. 411
ried with the endlefs Labour, he fhall own his Error.
In Sum, I obferve univerfally of thofe Reafon-
ings of Tacquet: Firft, That he every where begs
the Queftion, and commits vicious Circles, arguing
thus, A Property is not proximate, but remote, becaufie it can be demonftrated, i. e. becaufie there is a-
nother nigher , another is nigher, becaufie it may be
demonftrated that this Property conftitutes not an E-
quality of Reafons (i. e. cannot enter its Definition)
becaufe it differs firom it, is not clearly connected with
it, or is very much removed firom its Nature. And
fo every where.
Secondly, I note that neither he, nor moft others,
as far as I can judge, do fufficiently perceive the
Nature of a Definition ; by whom nothing is really
done, but a Name impofed upon a Thing, as it is
the Subject of an Affection evidently difcovered by
Senfe or Reafon: but they devife I know not what
abftrufe Natures, Effences and Formalities, which
can never be brought to Light. By which, if we
fearch the Thing to the quick, it will appear that
they underftand nothing but fome imperfect and indistinct Conceptions, or Significations, anfwering to
the customary Name of the Thing defined, which
are net to be received in the Sciences, and are unfit
for Demonftrations ; to which confequently no Definitions are requisite ; nay Definitions are to be
formed by fecluding and banishing thofe, and fub-
ftitutir-g for them certain Diftinct and clear Ideas
of Things ; appropriating Names to Things, as
far as they ere fubject to certain Affections conspicuous to the Senfe, or to the Underftanding.
I obferve Thirdly, That Tacquet, led by fuch Arguments, has affigned a Definition of equal Reafons
very vicious and ufelefs. For he fays, Reafons are
equal* when the Antecedent of the one contains, oris
contained in, its Confequent in the fame Manner as
the
| 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 411. |
| Format | tiff |
| Identifier | 1135_449 |
| 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. XXII. Mathematical Lectures. 411 ried with the endlefs Labour, he fhall own his Error. In Sum, I obferve univerfally of thofe Reafon- ings of Tacquet: Firft, That he every where begs the Queftion, and commits vicious Circles, arguing thus, A Property is not proximate, but remote, becaufie it can be demonftrated, i. e. becaufie there is a- nother nigher , another is nigher, becaufie it may be demonftrated that this Property conftitutes not an E- quality of Reafons (i. e. cannot enter its Definition) becaufe it differs firom it, is not clearly connected with it, or is very much removed firom its Nature. And fo every where. Secondly, I note that neither he, nor moft others, as far as I can judge, do fufficiently perceive the Nature of a Definition ; by whom nothing is really done, but a Name impofed upon a Thing, as it is the Subject of an Affection evidently difcovered by Senfe or Reafon: but they devife I know not what abftrufe Natures, Effences and Formalities, which can never be brought to Light. By which, if we fearch the Thing to the quick, it will appear that they underftand nothing but fome imperfect and indistinct Conceptions, or Significations, anfwering to the customary Name of the Thing defined, which are net to be received in the Sciences, and are unfit for Demonftrations ; to which confequently no Definitions are requisite ; nay Definitions are to be formed by fecluding and banishing thofe, and fub- ftitutir-g for them certain Diftinct and clear Ideas of Things ; appropriating Names to Things, as far as they ere fubject to certain Affections conspicuous to the Senfe, or to the Underftanding. I obferve Thirdly, That Tacquet, led by fuch Arguments, has affigned a Definition of equal Reafons very vicious and ufelefs. For he fays, Reafons are equal* when the Antecedent of the one contains, oris contained in, its Confequent in the fame Manner as the |
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