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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Side 135
... adding NM to both , LM is greater than NP . therefore if GH be greater than KO , LM is greater than NP . In like manner it may be fhewn that if GH be equal to KO , LM is equal to NP ; and if lefs , lefs . And in the cafe in which KO is ...
... adding NM to both , LM is greater than NP . therefore if GH be greater than KO , LM is greater than NP . In like manner it may be fhewn that if GH be equal to KO , LM is equal to NP ; and if lefs , lefs . And in the cafe in which KO is ...
Side 142
... added equal magnitudes , viz . to GB the two AG and F , and CH and E to HD ; AB and F together are greater than CD and E. Therefore if four magnitudes , & c . Q. E. D. PROP . F. THEOR . ATIOS which are compounded of the fame ratios ...
... added equal magnitudes , viz . to GB the two AG and F , and CH and E to HD ; AB and F together are greater than CD and E. Therefore if four magnitudes , & c . Q. E. D. PROP . F. THEOR . ATIOS which are compounded of the fame ratios ...
Side 179
... adding SR to each , the whole OB is equal to the whole XB . but XB is equal to TE , becaufe the base AE 8. 36. I , is equal to the base EB ; wherefore alfo TE is equal to OB . add XS to each , then the whole TS is equal to the whole ...
... adding SR to each , the whole OB is equal to the whole XB . but XB is equal to TE , becaufe the base AE 8. 36. I , is equal to the base EB ; wherefore alfo TE is equal to OB . add XS to each , then the whole TS is equal to the whole ...
Side 291
... added at the end of this Definition in all the copies , but are now left out as not belonging to the Definition , being only a Co- rollary from it . Proclus demonftrates it by conceiving one of the parts into which the diameter divides ...
... added at the end of this Definition in all the copies , but are now left out as not belonging to the Definition , being only a Co- rollary from it . Proclus demonftrates it by conceiving one of the parts into which the diameter divides ...
Side 292
... added . befides the tranflation from the Arabic has this case explicitely demonstrated . and Proclus acknowledges that the fecond part of Prop . 5. was added upon account of Prop . 7. but gives a ridiculous reason for it , " that it ...
... added . befides the tranflation from the Arabic has this case explicitely demonstrated . and Proclus acknowledges that the fecond part of Prop . 5. was added upon account of Prop . 7. but gives a ridiculous reason for it , " that it ...
Almindelige termer og sætninger
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 passager
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.