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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Σελίδα 31
... fore the angle ACB is equal to the angle CBD . and because the straight line BC meets the two straight lines AC , BD and makes , the alternate angles ACB , CBD equal to one another , AC is rallel to BD . and it was fhewn to be equal to ...
... fore the angle ACB is equal to the angle CBD . and because the straight line BC meets the two straight lines AC , BD and makes , the alternate angles ACB , CBD equal to one another , AC is rallel to BD . and it was fhewn to be equal to ...
Σελίδα 54
... fore the rectangle CF , FA , together with the fquare of AE is equal to the fquare of EB . and the fquares of BA , AE are equal to the fquare of EB , because the angle EAB is a right angle ; therefore the rectangle CF , A FA , together ...
... fore the rectangle CF , FA , together with the fquare of AE is equal to the fquare of EB . and the fquares of BA , AE are equal to the fquare of EB , because the angle EAB is a right angle ; therefore the rectangle CF , A FA , together ...
Σελίδα 64
... fore EF is equal to EG , the lefs to the greater , which is impoffible . therefore E is not the center of A G E B the circles ABC , CDG . Wherefore if two circles , & c . Q. E. D. IT PROP . VI . THEOR . two circles touch one another ...
... fore EF is equal to EG , the lefs to the greater , which is impoffible . therefore E is not the center of A G E B the circles ABC , CDG . Wherefore if two circles , & c . Q. E. D. IT PROP . VI . THEOR . two circles touch one another ...
Σελίδα 66
... fore the base FG is equal to the bafe FH . but befides FH no other ftraight line can be drawn from F to d . 4. 1 . d the circumference equal to FG . for E D H if there can , let it be FK , and because FK is equal to FG , and FG to FH ...
... fore the base FG is equal to the bafe FH . but befides FH no other ftraight line can be drawn from F to d . 4. 1 . d the circumference equal to FG . for E D H if there can , let it be FK , and because FK is equal to FG , and FG to FH ...
Σελίδα 67
... fore DA is the greatest ; and DE greater than DF , and DF than DC . and because MK , KD are greater b than MD , and MK is equal to MG , the remainder KD is greater than the remainder GD , that is , GD is C lefs than KD . and because MK ...
... fore DA is the greatest ; and DE greater than DF , and DF than DC . and because MK , KD are greater b than MD , and MK is equal to MG , the remainder KD is greater than the remainder GD , that is , GD is C lefs than KD . and because MK ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 73 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...
Σελίδα 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.
Σελίδα 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.
Σελίδα 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Σελίδα 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.
Σελίδα 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.