The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The first six books, together with the eleventh and twelfthF. Wingrave, 1804 |
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Resultat 6-10 av 100
Side 189
... planes . XII . A Pyramid is a folid figure contained by planes that are constituted betwixt one plane and one point above it in which they meet . XIII . A Prism is a folid figure contained by plane figures of which two that are oppofite ...
... planes . XII . A Pyramid is a folid figure contained by planes that are constituted betwixt one plane and one point above it in which they meet . XIII . A Prism is a folid figure contained by plane figures of which two that are oppofite ...
Side 191
... plane and See N. another part above it . OND If it be poffible , let AB part of the straight line ABC be in the plane , and the part BC above it . and since the straight line AB is in the plane , it can be produced in that plane . let ...
... plane and See N. another part above it . OND If it be poffible , let AB part of the straight line ABC be in the plane , and the part BC above it . and since the straight line AB is in the plane , it can be produced in that plane . let ...
Side 192
... plane BC the straight E line DFB . then two ftraight lines DEB , DFB have the fame extremities , and there- fore ... plane which passes through them , that is , to the plane in which they are . Let the ftraight line EF ftand at right ...
... plane BC the straight E line DFB . then two ftraight lines DEB , DFB have the fame extremities , and there- fore ... plane which passes through them , that is , to the plane in which they are . Let the ftraight line EF ftand at right ...
Side 193
... plane . But a straight line is at right angles to a plane when it makes right angles with every straight line which meets it in that plane f . therefore EF f . 3. Def.11 . is at right angles to the plane in which are AB , CD . Wherefore ...
... plane . But a straight line is at right angles to a plane when it makes right angles with every straight line which meets it in that plane f . therefore EF f . 3. Def.11 . is at right angles to the plane in which are AB , CD . Wherefore ...
Side 194
... plane passing thro ' them ; and there - A c.3.Def.11 . fore makes right angles with every C F D B E ftraight line meeting it in that plane ; but BF which is in that plane meets it , therefore the angle ABF is a right angle ; but the ...
... plane passing thro ' them ; and there - A c.3.Def.11 . fore makes right angles with every C F D B E ftraight line meeting it in that plane ; but BF which is in that plane meets it , therefore the angle ABF is a right angle ; but the ...
Vanlige uttrykk og setninger
alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle becauſe the ratio bifected Book XI cafe circle ABCD circumference cone conſtruction cylinder defcribed demonſtrated drawn EFGH equal angles equiangular equimultiples Euclid excefs faid fame multiple fame ratio fecond fegment fhall fhewn fides fides BA fimilar fince firft firſt folid angle fore fquare fquare of AC given angle given in fpecies given in magnitude given in pofition given magnitude given ratio given ſtraight line gnomon greater join lefs leſs likewife line BC muſt oppofite parallel parallelepipeds parallelogram perpendicular plane angles PROP Propofition pyramid rectangle contained rectilineal figure right angles ſame ſhall ſpace ſphere ſquare ſtraight line AB THEOR theſe thro tiple triangle ABC wherefore
Populære avsnitt
Side 157 - D ; wherefore the remaining angle at C is equal to the remaining angle at F ; Therefore the triangle ABC is equiangular to the triangle DEF. Next, let each of the angles at C, F be not less than a right angle ; the triangle ABC is also, in this case, equiangular to the triangle DEF.
Side 24 - ... be equal, each to each ; and also the third angle of the one to the third angle of the other. Let ABC, DEF be two triangles which have the angles ABC, ECA equal to the angles DEF, EFD, viz.
Side 45 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Side 73 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...
Side 163 - 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.
Side 81 - ELF. Join BC, EF ; and because the circles ABC, DEF are equal, the straight lines drawn from their centres are equal: therefore the two sides BG, GC, are equal to the two EH, HF ; and the angle at G is equal to the angle at H ; therefore the base BC is equal (4.
Side 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Side 80 - EA : and because AD is equal to DC, and DE common to the triangles ADE, CDE, the two sides AD, DE are equal to the two CD, DE, each to each ; and the angle ADE is equal to the angle CDE, for each of them is a right angle ; therefore the base AE is equal (4.
Side 36 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.