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an:
Lect. XV. Mathematical Lectures. 277
that is accounted as efpecially known, and perfectly dilcovered, whofe Reafon is expreffed in
Numbers to fomething before known;, though
not unworthy our Confideration, I now pafs by in
order to hasten to fomething elfe. So far I have
touched upon the particular Knowledge of Quantities : But
Fourthly* Every Quantity is faid to b? after a
Sort known and determined (as we have faid
above; whofe general Nature we comprehend,
though we are ignorant of its particular Quantity, or do not confider it. Thus we know how
a Radius is affected in a Circle, or a Side in a
Square, though we are ignorant, or neglect the
Quantity of this or that particular Radius of a
Circle, or Side of a Square. Efpecially thofe
Quantities are known which are laid down for the
Generation of others, and confequently determine
every Thing following that Generation, and from
thence naturally challenge the Place of a Meafure.
As if a Circle be fuppofed to be generated from
the Revolution of its Radius, a Square from the
drawing of its Side into itfelf, or from its direct
parallel Motion; then becaufe the Quantity and
Pofition of all other Lines in a Circle or a Square
depend upon the Quantity of the Radius of the
one or Side of the other with fuch a Motion ;
confequently thofe are not undefervedly reckoned
as primarily known : and are general primitive
Meafures, from a Comparifon with which, the
Things which obtain a fimilar Situation perpetually determinate in refpect of them, are confequently known by a General Method , i. e. the
conltant Proportion may be known of thefe to
thofe, and therefore the particular Quantity of
thefe may be alfo known, from a Suppofition that
the particular Quantity of thofe is known. For,
if the Proportion of two Quantities be found, the
T 3 one
I
| 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 277. |
| Format | tiff |
| Identifier | 1135_315 |
| 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 | an: Lect. XV. Mathematical Lectures. 277 that is accounted as efpecially known, and perfectly dilcovered, whofe Reafon is expreffed in Numbers to fomething before known;, though not unworthy our Confideration, I now pafs by in order to hasten to fomething elfe. So far I have touched upon the particular Knowledge of Quantities : But Fourthly* Every Quantity is faid to b? after a Sort known and determined (as we have faid above; whofe general Nature we comprehend, though we are ignorant of its particular Quantity, or do not confider it. Thus we know how a Radius is affected in a Circle, or a Side in a Square, though we are ignorant, or neglect the Quantity of this or that particular Radius of a Circle, or Side of a Square. Efpecially thofe Quantities are known which are laid down for the Generation of others, and confequently determine every Thing following that Generation, and from thence naturally challenge the Place of a Meafure. As if a Circle be fuppofed to be generated from the Revolution of its Radius, a Square from the drawing of its Side into itfelf, or from its direct parallel Motion; then becaufe the Quantity and Pofition of all other Lines in a Circle or a Square depend upon the Quantity of the Radius of the one or Side of the other with fuch a Motion ; confequently thofe are not undefervedly reckoned as primarily known : and are general primitive Meafures, from a Comparifon with which, the Things which obtain a fimilar Situation perpetually determinate in refpect of them, are confequently known by a General Method , i. e. the conltant Proportion may be known of thefe to thofe, and therefore the particular Quantity of thefe may be alfo known, from a Suppofition that the particular Quantity of thofe is known. For, if the Proportion of two Quantities be found, the T 3 one I |
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