Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Page 8
... wherefore the remain- der A L is equal to the remainder B G [ by axiom 3. ] . But it has been proved , that the right line BC is equal to the right line BG ; therefore each of the right lines AL , BC , is equal to the right line BG ...
... wherefore the remain- der A L is equal to the remainder B G [ by axiom 3. ] . But it has been proved , that the right line BC is equal to the right line BG ; therefore each of the right lines AL , BC , is equal to the right line BG ...
Page 11
... wherefore [ by prop . 4. ] the base F C will be equal to the base GB ; and the triangle AFC equal to the triangle A G B and the remaining angles fhall be equal to the remaining angles , each to each , which are oppofite to the equal ...
... wherefore [ by prop . 4. ] the base F C will be equal to the base GB ; and the triangle AFC equal to the triangle A G B and the remaining angles fhall be equal to the remaining angles , each to each , which are oppofite to the equal ...
Page 13
... wherefore the bafe DC will be equal to the bafe A B , and the triangle ABC will be equal to the triangle DCB ; the greater to the lefs ; which is abfurd . 1 . C Therefore the right line A B is not unequal to the right line A C ; they ...
... wherefore the bafe DC will be equal to the bafe A B , and the triangle ABC will be equal to the triangle DCB ; the greater to the lefs ; which is abfurd . 1 . C Therefore the right line A B is not unequal to the right line A C ; they ...
Page 20
... Wherefore it neceffarily follows , that both the angles A B D , A B C are equal to two right angles , the one being just as much above a right angle , as the other wants of one . PROP . XIV . THEOR . If at a point in any right line two ...
... Wherefore it neceffarily follows , that both the angles A B D , A B C are equal to two right angles , the one being just as much above a right angle , as the other wants of one . PROP . XIV . THEOR . If at a point in any right line two ...
Page 23
... wherefore the angles A B C , B C A are 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 ...
... wherefore the angles A B C , B C A are 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 ...
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...