Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth BooksJ. Rivington, 1765 - 464 páginas |
Dentro del libro
Resultados 6-10 de 32
Página 376
... pyramid DEFH ; the prifm whofe bafe is the par- allelogram KLX B , and the right line M o oppofite to it , will be ... pyramid ABCG , to the two prifms in the pyramid DEFH . So likewise if the pyramids made by the divifion aforefaid be ...
... pyramid DEFH ; the prifm whofe bafe is the par- allelogram KLX B , and the right line M o oppofite to it , will be ... pyramid ABCG , to the two prifms in the pyramid DEFH . So likewise if the pyramids made by the divifion aforefaid be ...
Página 377
... pyramid OM NG to the two prifms that are in the pyramid STVH . But as the bafe OMN is to the bafe s T v , so is the base A B C to the base DEF . And therefore as the base ABC is to the bafe DEF , fo are the two prifms in the pyramid ...
... pyramid OM NG to the two prifms that are in the pyramid STVH . But as the bafe OMN is to the bafe s T v , so is the base A B C to the base DEF . And therefore as the base ABC is to the bafe DEF , fo are the two prifms in the pyramid ...
Página 378
... pyramid ABCG to the pyramid DEFH . For if it be not fo , it will be as the bafe ABC is to the bafe DEF , fo is the pyramid A BCG to fome folid either lefs or greater than the pyramid DEFH . Firft let it be to a folid less , as y ; and ...
... pyramid ABCG to the pyramid DEFH . For if it be not fo , it will be as the bafe ABC is to the bafe DEF , fo is the pyramid A BCG to fome folid either lefs or greater than the pyramid DEFH . Firft let it be to a folid less , as y ; and ...
Página 379
... pyramid A BCG But as the folid Y is to the pyra . mid ABCG , fo is the pyramid DEFH to fome folid lefs than the pyramid ABCG , as has been but now demonftra- ted : And there- fore as the base DEF , is ' to the bafe ABC , fo is the pyramid ...
... pyramid A BCG But as the folid Y is to the pyra . mid ABCG , fo is the pyramid DEFH to fome folid lefs than the pyramid ABCG , as has been but now demonftra- ted : And there- fore as the base DEF , is ' to the bafe ABC , fo is the pyramid ...
Página 380
... pyramid ACDM ; and by compofi- tion [ by 18. 5. ] as the trapezium ABCD is to the trian- gle ACD , fo is the pyramid ABCDM to the pyramid ABCM . But as the triangle ACD is to the triangle ADE , fo is the pyramid ACDM to the pyramid ADEM ...
... pyramid ACDM ; and by compofi- tion [ by 18. 5. ] as the trapezium ABCD is to the trian- gle ACD , fo is the pyramid ABCDM to the pyramid ABCM . But as the triangle ACD is to the triangle ADE , fo is the pyramid ACDM to the pyramid ADEM ...
Otras ediciones - Ver todas
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Sin vista previa disponible - 2023 |
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Sin vista previa disponible - 2023 |
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Sin vista previa disponible - 2016 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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...
Página 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.
Página 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.
Página 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.
Página 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.
Página 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...
Página 110 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.
Página 130 - When you have proved that the three angles of every triangle are equal to two right angles...
Página 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...