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 113
... Excess of the first above the second , is to the second , as the Excess of the third above the fourth , is to the fourth . 17th Prop . Book 5th . XVII . Convertendo , by Converfion ; when there are four proportionals , and it is ...
... Excess of the first above the second , is to the second , as the Excess of the third above the fourth , is to the fourth . 17th Prop . Book 5th . XVII . Convertendo , by Converfion ; when there are four proportionals , and it is ...
Page 136
... excess above the second , as the third to its excess above the fourth , Let AB be to BE , as CD to DF ; then BA is to AE , as DC to CF. Because AB is to BE , as CD to DF , by E division , AE is to EB , as CF to FD ; and by inversion b ...
... excess above the second , as the third to its excess above the fourth , Let AB be to BE , as CD to DF ; then BA is to AE , as DC to CF. Because AB is to BE , as CD to DF , by E division , AE is to EB , as CF to FD ; and by inversion b ...
Page 141
... excess of the first and fifth shall be to the second , as the excess of the third and fixth to the fourth , the Demonstration of this is the Book V. fame with that of the Propofition , if OF EUCLID . 14.
... excess of the first and fifth shall be to the second , as the excess of the third and fixth to the fourth , the Demonstration of this is the Book V. fame with that of the Propofition , if OF EUCLID . 14.
Page 178
... parallelogram KLMN equal to the excess of EF above C , and similar and fimi- larly situated to D ; but D is similar to EF , therefore d alfo KM is fimilar to EF . let KL be the homologous fide. d . 21. 6 . e . 4. 1 . 178 THE ELEMENTS.
... parallelogram KLMN equal to the excess of EF above C , and similar and fimi- larly situated to D ; but D is similar to EF , therefore d alfo KM is fimilar to EF . let KL be the homologous fide. d . 21. 6 . e . 4. 1 . 178 THE ELEMENTS.
Page 212
... excess of R II . the square of AB above the square of LX , and make RX equal to its fide , and join RL , RM , RN . because RX is perpendicular to the plane of the m . 3. Def . circle LMN , it is perpendicular to each of the straight ...
... excess of R II . the square of AB above the square of LX , and make RX equal to its fide , and join RL , RM , RN . because RX is perpendicular to the plane of the m . 3. Def . circle LMN , it is perpendicular to each of the straight ...
Common terms and phrases
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
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 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.
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.