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426 Mathematical Lectures. Lect. XXIIL
interpofe, as has been often inculcated, that there
is no fuch Thing as a Nature of Proportionals
prior to the faid Property, nor is it needful for us
to know any Thing before that Definition concerning them, at leaft diftinctly and certainly. But
he goes on, For firom hence, becaufie four Equimultiples of Magnitudes have that Condition ofi Excefs
or Defect, it is not perceived when* or how* they
are Proportionals* if the Antecedents do together exceed* or fall fhort of their Confiequents, neither ifi the
Exceffes be equal to one another, or no. Which
Words of Borellus feem very obfeure and ambiguous; but whatfoever they fignify I am certain
they can no Way hurt us. For from hence, becaufe four Equimultiples of Quantities have that
Condition, it is plainly perceived that the Name of
Proportionals agrees with them, nor is it any Matter, what elfe is perceived.
There remains one Objection to be removed
after all Thefe, which is the moft weighty of all
the reft, if it do but depend upon a true Suppofition.
Nor finally (fays he) can the leaft Knowledge be gathered firom the fiaid Property, viz. that to make
four Magnitudes proportional* when the firft exceeds
the fiecond* the third Magnitude muft neceffarily exceed the fourth* as Clavius confieffes in Prop. XVI.
lib. py. Elem. I anlwer, Firft* That this Confeffion
feems to be falfly fixed upon Clavius* for in the
Place cited I can find no fuch Thing. Secondly,
How has Euclid demonftrated, if not from that
Property, having premifed no other Definition of
Proportionals? Certainly he has demonstrated by
it, though not immediately. And who knows not
that in moft Demonftrations the Property of the
Subject is not deduced immediately from its Definition ? it being fufficient to be done mediately by
other Properties before derived from the Definition
of the Subject. Thirdly* I add, though Clavius
djd
| 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 426. |
| Format | tiff |
| Identifier | 1135_464 |
| 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 | 426 Mathematical Lectures. Lect. XXIIL interpofe, as has been often inculcated, that there is no fuch Thing as a Nature of Proportionals prior to the faid Property, nor is it needful for us to know any Thing before that Definition concerning them, at leaft diftinctly and certainly. But he goes on, For firom hence, becaufie four Equimultiples of Magnitudes have that Condition ofi Excefs or Defect, it is not perceived when* or how* they are Proportionals* if the Antecedents do together exceed* or fall fhort of their Confiequents, neither ifi the Exceffes be equal to one another, or no. Which Words of Borellus feem very obfeure and ambiguous; but whatfoever they fignify I am certain they can no Way hurt us. For from hence, becaufe four Equimultiples of Quantities have that Condition, it is plainly perceived that the Name of Proportionals agrees with them, nor is it any Matter, what elfe is perceived. There remains one Objection to be removed after all Thefe, which is the moft weighty of all the reft, if it do but depend upon a true Suppofition. Nor finally (fays he) can the leaft Knowledge be gathered firom the fiaid Property, viz. that to make four Magnitudes proportional* when the firft exceeds the fiecond* the third Magnitude muft neceffarily exceed the fourth* as Clavius confieffes in Prop. XVI. lib. py. Elem. I anlwer, Firft* That this Confeffion feems to be falfly fixed upon Clavius* for in the Place cited I can find no fuch Thing. Secondly, How has Euclid demonftrated, if not from that Property, having premifed no other Definition of Proportionals? Certainly he has demonstrated by it, though not immediately. And who knows not that in moft Demonftrations the Property of the Subject is not deduced immediately from its Definition ? it being fufficient to be done mediately by other Properties before derived from the Definition of the Subject. Thirdly* I add, though Clavius djd |
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