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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Página 31
... parallelograms are equal to one another , and the diameter bisects them , that is , divides them into two equal ... parallelogram , of which BC is a diameter . the opposite sides and angles of the figure are equal to one ano- ther ...
... parallelograms are equal to one another , and the diameter bisects them , that is , divides them into two equal ... parallelogram , of which BC is a diameter . the opposite sides and angles of the figure are equal to one ano- ther ...
Página 32
... parallelogram ABCD shall be equal to the parallelogram EBCF . If the fides AD , DF of the parallelograms ABCD , DBCF oppo- fite to the base BC , be terminated in the fame point D ; it is plain that each a . 34. I. of the parallelograms ...
... parallelogram ABCD shall be equal to the parallelogram EBCF . If the fides AD , DF of the parallelograms ABCD , DBCF oppo- fite to the base BC , be terminated in the fame point D ; it is plain that each a . 34. I. of the parallelograms ...
Página 33
... parallelogram EFGH is equal to the fame EBCH . therefore also the parallelogram ABCD is equal to EFGH . Wherefore parallelograms , & c . Q. E. D. T PROP . XXXVII . THEOR . RIANGLES upon the same base , and between the same parallels ...
... parallelogram EFGH is equal to the fame EBCH . therefore also the parallelogram ABCD is equal to EFGH . Wherefore parallelograms , & c . Q. E. D. T PROP . XXXVII . THEOR . RIANGLES upon the same base , and between the same parallels ...
Página 35
... . Q. E. D. IF PROP . XLI . THEOR . Fa parallelogram and triangle be upon the fame base , and between the fame parallels ; the paral- lelogram shall be double of the triangle Book I. a . 37. 1 . b . 34. C2 OF EUCLID . 35.
... . Q. E. D. IF PROP . XLI . THEOR . Fa parallelogram and triangle be upon the fame base , and between the fame parallels ; the paral- lelogram shall be double of the triangle Book I. a . 37. 1 . b . 34. C2 OF EUCLID . 35.
Página 36
... parallelogram ABCD and the triangle EBC be upon the fame base BC , and between the fame parallels BC , AE ; the parallelogram ABCD is double of the A triangle EBC . DE Join AC ; then the triangle ABC is equal a to the triangle EBC ...
... parallelogram ABCD and the triangle EBC be upon the fame base BC , and between the fame parallels BC , AE ; the parallelogram ABCD is double of the A triangle EBC . DE Join AC ; then the triangle ABC is equal a to the triangle EBC ...
Términos y frases comunes
alſo altitude angle ABC angle BAC baſe BC BC is equal BC is given becauſe the angle becauſe the ratio biſected Book XI cafe cauſe circle ABCD circumference cone conſtruction cylinder demonſtrated deſcribed diameter drawn EFGH equal angles equiangular equimultiples Euclid exceſs fame multiple fame ratio fame reaſon fides fimilar firſt folid angle fore given angle given in magnitude given in poſition given in ſpecies given magnitude given ratio given ſtraight line gnomon greater join leſs likewife oppoſite parallel parallelepipeds parallelogram paſs perpendicular plane angles priſm PROP proportionals Propoſition pyramid rectangle contained rectilineal figure right angles ſame ſecond ſegment ſhall ſhall be equal ſhewn ſide ſolid ſome ſpace ſphere ſquare of AC ſtraight line AC THEOR theſe thoſe thro triangle ABC vertex wherefore
Pasajes populares
Página 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.
Página 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.
Página 1 - The circumference of every circle is supposed to be divided into 360 equal parts called degrees, and each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds, and these into thirds, fourths, &c.
Página 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.
Página 73 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...
Página 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.
Página 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.
Página 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Página 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.
Página 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.