Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Page 11
... angles at the bafe of ifofceles triangles are equal to one another ; and the equal right lines being pro- duced , the angles under the base shall be equal to one another x Let ABC be an ifofceles triangle , having the fide A B equal to ...
... angles at the bafe of ifofceles triangles are equal to one another ; and the equal right lines being pro- duced , the angles under the base shall be equal to one another x Let ABC be an ifofceles triangle , having the fide A B equal to ...
Page 12
... equal to the remaining angle ACB ; and they are at the bafe of the triangle A B C. But alfo it has been de- monftrated , that the angle F B C is equal to the angle G C B , and they are under the base . Therefore the angles ... equal to one ...
... equal to the remaining angle ACB ; and they are at the bafe of the triangle A B C. But alfo it has been de- monftrated , that the angle F B C is equal to the angle G C B , and they are under the base . Therefore the angles ... equal to one ...
Page 13
... 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 are confequently equal . Therefore if two angles of a triangle be equal , the fides ...
... 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 are confequently equal . Therefore if two angles of a triangle be equal , the fides ...
Page 18
... equal to the base EF : therefore the angle D C F is equal [ by prop . 8. ] to the angle ECF ; and thefe are adjacent angles . But when a right line standing upon a right line makes the adjacent angles equal to one an- -A D C E B other ...
... equal to the base EF : therefore the angle D C F is equal [ by prop . 8. ] to the angle ECF ; and thefe are adjacent angles . But when a right line standing upon a right line makes the adjacent angles equal to one an- -A D C E B other ...
Page 19
... equal to two right angles . For if the angle C B A be equal to the angle A B D ; then will they be both right angles [ by def . 10. ] but if not , let the right line E B be drawn from the point B at right angles to the right line DC ...
... equal to two right angles . For if the angle C B A be equal to the angle A B D ; then will they be both right angles [ by def . 10. ] but if not , let the right line E B be drawn from the point B at right angles to the right line DC ...
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...