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 - Trigonometry |
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Page 9
... because AB is equal to DE . and AB coin- ciding with DE , AC fhall coincide with DF , because the angle BAC full on is equal to the angle EDF . wherefore alfo the point C fhall coin- cide with the point F , because the straight line AC ...
... because AB is equal to DE . and AB coin- ciding with DE , AC fhall coincide with DF , because the angle BAC full on is equal to the angle EDF . wherefore alfo the point C fhall coin- cide with the point F , because the straight line AC ...
Page 17
... because the ftraight line Book 1 . AB makes angles with the straight line CBE , upon one fide of it , the angles ABC ... Because the straight line AE makes with CD the angles CEA , AED , these angles are together equal a to two right ...
... because the ftraight line Book 1 . AB makes angles with the straight line CBE , upon one fide of it , the angles ABC ... Because the straight line AE makes with CD the angles CEA , AED , these angles are together equal a to two right ...
Page 19
... Because AC is greater than AB ; make a AD equal to AB , and join BD . and becaufe ADB B is the exterior angle of the tri- b A a . 3. I. C. 5. I. angle BDC , it is greater than the interior and oppofite angle b . 16. 1 . DCB . but ADB is ...
... Because AC is greater than AB ; make a AD equal to AB , and join BD . and becaufe ADB B is the exterior angle of the tri- b A a . 3. I. C. 5. I. angle BDC , it is greater than the interior and oppofite angle b . 16. 1 . DCB . but ADB is ...
Page 31
... because the straight line BC meets the two straight lines AC , BD and makes , the alternate angles ACB , CBD equal ... Because AB is parallel to CD , and BC meets them , the alternate angles ABC , BCD are equal to one another , and ...
... because the straight line BC meets the two straight lines AC , BD and makes , the alternate angles ACB , CBD equal ... Because AB is parallel to CD , and BC meets them , the alternate angles ABC , BCD are equal to one another , and ...
Page 34
... because the diameter AB bifects it ; and the triangle DBC is the half of the parallelogram DBCF , because the diameter DC bifects it . but the halves of equal things are d . 7. Ax . equal d ; therefore the triangle ABC is equal to the ...
... because the diameter AB bifects it ; and the triangle DBC is the half of the parallelogram DBCF , because the diameter DC bifects it . but the halves of equal things are d . 7. Ax . equal d ; therefore the triangle ABC is equal to the ...
Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page 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.
Page 73 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...
Page 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.
Page 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.
Page 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Page 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.
Page 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.