Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Page 6
... less than both the angles A E F , CFE on the left ; and fince two different right lines cannot be drawn from the fame point out of a given right line parallel to that given right line ; and fince it is demonftrated at prop . 28. lib . 1 ...
... less than both the angles A E F , CFE on the left ; and fince two different right lines cannot be drawn from the fame point out of a given right line parallel to that given right line ; and fince it is demonftrated at prop . 28. lib . 1 ...
Page 12
... less important and useful part of the propofition , and there- fore the former part deferved the first place . And if a propo- fition be not all Euclid's , because it is not useful in all its parts , other propofitions of thefe elements ...
... less important and useful part of the propofition , and there- fore the former part deferved the first place . And if a propo- fition be not all Euclid's , because it is not useful in all its parts , other propofitions of thefe elements ...
Page 23
... less than two right angles . After the fame way we demon- ftrate that the angles B A C , A C B are less than two right angles ; as alfo the angles C A B , A B C. Therefore any two angles of every triangle taken toge- ther , are less ...
... less than two right angles . After the fame way we demon- ftrate that the angles B A C , A C B are less than two right angles ; as alfo the angles C A B , A B C. Therefore any two angles of every triangle taken toge- ther , are less ...
Page 24
... less than the fide A B ; for then the angle A B C would be [ by prop . 18. ] lefs than the angle A C B. is not lefs ; nor therefore will the fide A C be less than the fide A B. But it has been demonstrated not to be equal to it ...
... less than the fide A B ; for then the angle A B C would be [ by prop . 18. ] lefs than the angle A C B. is not lefs ; nor therefore will the fide A C be less than the fide A B. But it has been demonstrated not to be equal to it ...
Page 25
... less than the two remaining fides of the triangle , but will contain a greater angle . For from the ends B , C , of one of the fides B C of the tri- angle ABC , let two right lines B D , CD be conftituted within the triangle : I fay ...
... less than the two remaining fides of the triangle , but will contain a greater angle . For from the ends B , C , of one of the fides B C of the tri- angle ABC , let two right lines B D , CD be conftituted within the triangle : I fay ...
Other editions - View all
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory No preview available - 2023 |
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory No preview available - 2023 |
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory No preview available - 2016 |
Common terms and phrases
A B C D alfo alſo angle ABC becauſe the angle bifected centre circle A B C circumference cone confequent cylinder defcribed demonftrated diameter equal angles equiangular equimultiples Euclid EUCLID's ELEMENTS fame altitude fame multiple fame ratio fame reafon fecond fegment femidiameter fhall fides A B fimilar fince firft firſt fixth folid angle folid parallelepipedon fome fphere ftand given circle given right line given triangle greater infcribed interfect join leffer lefs leſs parallel parallelogram perpendicular polygon prifm PROP propofition proportional pyramid rectangle contained regular polygon remaining angle right angles right line A B right lined figure right-lined SCHOLIUM ſquare thefe THEOR theſe thofe thoſe trapezium triangle ABC twice the fquare vertex the point Wherefore whofe bafe whoſe baſe
Popular passages
Page 247 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 30 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Page 248 - But it was proved that the angle AGB is equal to the angle at F ; therefore the angle at F is greater than a right angle : But by the hypothesis, it is less than a right angle ; which is absurd.
Page 18 - When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands.
Page 32 - Let the straight line EF, which falls upon the two straight lines AB, CD, make the alternate angles AEF, EFD equal to one another; AB is parallel to CD.
Page 56 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 391 - KL: but the cylinder CM is equal to the cylinder EB, and the axis LN to the axis GH; therefore as the cylinder EB to...
Page 110 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.
Page 130 - When you have proved that the three angles of every triangle are equal to two right angles...
Page 183 - FK : in the same manner it may be demonstrated, that FL, FM, FG are each of them equal to FH, or FK : therefore the five straight lines FG, FH, FK, FL, FM are equal to one another : wherefore the circle described from the centre F, at the distance of...