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Lect. XXI. Mathematical Lectures. 391
ner is its Bafis encreafed or multiplied : as alfo if
the former Increment or Multiple be greater than
the latter, the one Bafis anfwering to it will be greater than the Bafis of the other Increment or Multiple;
if that be leffer this will be leffer ; if that be equal
this will be alfo equal. Again, any two Wholes,
with their aliquot Parts, becaufe of that affumed
Condition of Likenefis* are fo connected, that all the
Multiplications of the one do include and convey
along with them, the like Multiplications of the o-
ther refpectively ; and if the Multiple of the former
Whole exceed, fall fhort, or equal the Multiple of
the latter ; then the Multiple of the Parts of the former will alfo do the fime with the Multiple of the
Parts of the latter. This when our Author confi-
der'd, and moreover found it to happen otherwife
in Quantities otherwife affected, ex. gr. as we fhall
fhew hereafter, in Triangles of a different Height,
from the Excefs of the one the fame Way multiplied
with its Bafis above the Multiple of the other is never infer'd the Excefs of it's Bafis above the Bafis of
the other the fame Way multiplied with the other :
neither if the Wholes be compared with their unlike
Parts, from thence becaufe the former equally multiplied with its Parts exceeds fome Multiple of the
latter, will it any Way follow that therefore the
Multiple of the Parts of the former exceeds the Parts
of the latter equally multiplied with its Whole ?
Thofe Things, I fay again, when Euclid* or whoever elfe was the Author of thefe Definitions, obler -
ved and faw the faid Property to agree with all
Kind of Quantities promifcuoully, whether com-
menfurate or incommenfurate, tho' no Confideration of any Commenfurability or Incommenfurability
there intervenes ; hence he thought that the mutual
Refpects to one another of the Reafons, happening
to Quantities fo affected, are to be eftimated and
defined from it, Clavius thinks that our Author,
C c 4 wh
| 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 391. |
| Format | tiff |
| Identifier | 1135_429 |
| 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. XXI. Mathematical Lectures. 391 ner is its Bafis encreafed or multiplied : as alfo if the former Increment or Multiple be greater than the latter, the one Bafis anfwering to it will be greater than the Bafis of the other Increment or Multiple; if that be leffer this will be leffer ; if that be equal this will be alfo equal. Again, any two Wholes, with their aliquot Parts, becaufe of that affumed Condition of Likenefis* are fo connected, that all the Multiplications of the one do include and convey along with them, the like Multiplications of the o- ther refpectively ; and if the Multiple of the former Whole exceed, fall fhort, or equal the Multiple of the latter ; then the Multiple of the Parts of the former will alfo do the fime with the Multiple of the Parts of the latter. This when our Author confi- der'd, and moreover found it to happen otherwife in Quantities otherwife affected, ex. gr. as we fhall fhew hereafter, in Triangles of a different Height, from the Excefs of the one the fame Way multiplied with its Bafis above the Multiple of the other is never infer'd the Excefs of it's Bafis above the Bafis of the other the fame Way multiplied with the other : neither if the Wholes be compared with their unlike Parts, from thence becaufe the former equally multiplied with its Parts exceeds fome Multiple of the latter, will it any Way follow that therefore the Multiple of the Parts of the former exceeds the Parts of the latter equally multiplied with its Whole ? Thofe Things, I fay again, when Euclid* or whoever elfe was the Author of thefe Definitions, obler - ved and faw the faid Property to agree with all Kind of Quantities promifcuoully, whether com- menfurate or incommenfurate, tho' no Confideration of any Commenfurability or Incommenfurability there intervenes ; hence he thought that the mutual Refpects to one another of the Reafons, happening to Quantities fo affected, are to be eftimated and defined from it, Clavius thinks that our Author, C c 4 wh |
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