Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Page 26
... less than the two remaining fides of the tri- angle , but will contain a greater angle . Which was to be demonftrated . PROP . XXII . PROBL . To conftitute a triangle , whofe fides fhall be equal to three given right lines : but any two ...
... less than the two remaining fides of the tri- angle , but will contain a greater angle . Which was to be demonftrated . PROP . XXII . PROBL . To conftitute a triangle , whofe fides fhall be equal to three given right lines : but any two ...
Page 30
... less than the base EF : but it is not ; therefore the angle B A C is not lefs than the angle E D F. But it has been proved not be equal to it neither . Wherefore the angle B A C is greater than the angle E D F. If therefore two ...
... less than the base EF : but it is not ; therefore the angle B A C is not lefs than the angle E D F. But it has been proved not be equal to it neither . Wherefore the angle B A C is greater than the angle E D F. If therefore two ...
Page 35
... less than two right an- gles . Now let AC be cut into halves , or otherwife , in E : equal to E A let be put A F , and to EC , CG ; then draw FG . Again , let FG be cut in half in H , and equal to HF let be put F B , and to HG , GD ...
... less than two right an- gles . Now let AC be cut into halves , or otherwife , in E : equal to E A let be put A F , and to EC , CG ; then draw FG . Again , let FG be cut in half in H , and equal to HF let be put F B , and to HG , GD ...
Page 48
... less than two right angles . But right lines infinitely produced from angles lefs than two right angles [ by ax . 11. ] will meet one another . Let them be produced [ by poft . 2. ] meeting at K , and thro ' K draw [ by prop . 31. ] KL ...
... less than two right angles . But right lines infinitely produced from angles lefs than two right angles [ by ax . 11. ] will meet one another . Let them be produced [ by poft . 2. ] meeting at K , and thro ' K draw [ by prop . 31. ] KL ...
Page 53
... less than any other two right lines CH , DH taken toge- ther , drawn from the H I E B G given points C , D to any other point н taken in the right line A B. For from one of the given points , as D , [ by 12. 1. ] draw the right line D I ...
... less than any other two right lines CH , DH taken toge- ther , drawn from the H I E B G given points C , D to any other point н taken in the right line A B. For from one of the given points , as D , [ by 12. 1. ] draw the right line D I ...
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...