Book,  Chapter

 1      I,  I    |         be said that mathematical demonstrations, and other truths that are
 2      I,  I    |           maxims and mathematical demonstrations are in this different: that
 3      I,  I    |         And thus all mathematical demonstrations, as well as first principles,
 4      I,  III  |          expect undeniable cogent demonstrations, unless I may be allowed
 5     II,  XVI  |           extension?~4. Therefore demonstrations in numbers the most precise.
 6     II,  XVI  |        makes me apt to think that demonstrations in numbers, if they are
 7     IV,  I    |     ground it is, that particular demonstrations in mathematics afford general
 8     IV,  II   |       embrace often falsehood for demonstrations.~8. Hence the mistake, ex
 9     IV,  IV   |      strongholds of truth, as the demonstrations of Euclid. That an harpy
10     IV,  IV   |          those figures: but their demonstrations, which depend on their ideas,
11     IV,  IV   |            the properties of, and demonstrations about that idea will be
12     IV,  IV   |       drawn, the consequences and demonstrations are plain and clear. Just
13     IV,  VII  |        got the knowledge of those demonstrations, but by finding out intermediate
14     IV,  VII  | propositions; and is clear in the demonstrations above mentioned about a
15     IV,  VII  |         manifest.~16. Instance in demonstrations about man, which can only
16     IV,  VIII |          this method one may make demonstrations and undoubted propositions
17     IV,  XII  |          notions for scientifical demonstrations. In the knowledge of bodies,
18     IV,  XII  |       method who first made these demonstrations, can never sufficiently
19     IV,  XVII |          perceive in mathematical demonstrations, that the knowledge gained
20     IV,  XVII |          looked on several of the demonstrations of ancient mathematicians,
21     IV,  XVII |       overlooked. This makes some demonstrations long and perplexed, and
22     IV,  XVIII|           deductions of reason in demonstrations we need not the assistance