The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth. The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected : and Some of Euclid's Demonstrations Restored : Also the Book of Euclid's Data, in Like Manner CorrectedJ. Nourse, London, 1781 - 520 sider |
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Side 32
... firft let thofe fides be equal which are adjacent to the angles that are equal in the two triangles , viz . BC to EF ; the other A fides fhall be equal , G cach to each , viz . AB to DE , and AC to DF ; and the third angle BAC to the ...
... firft let thofe fides be equal which are adjacent to the angles that are equal in the two triangles , viz . BC to EF ; the other A fides fhall be equal , G cach to each , viz . AB to DE , and AC to DF ; and the third angle BAC to the ...
Side 85
... firft is double of GDB a part of the other ; therefore the re- G maining angle BEC is double of the remaining angle BDC . Therefore the angle at the centre , & c . Q. E. D. D E B C PROP . XXI . THEOR . HE angles in the fame fegment of a ...
... firft is double of GDB a part of the other ; therefore the re- G maining angle BEC is double of the remaining angle BDC . Therefore the angle at the centre , & c . Q. E. D. D E B C PROP . XXI . THEOR . HE angles in the fame fegment of a ...
Side 86
... firft cafe : For the fame reafon , becaufe CBED is greater than a femicircle , the angles CAD , CED are equal : Therefore the whole angle BAD is equal to the C whole angle BED . Wherefore the angles in the fame fegment , & c . Q. E. D. ...
... firft cafe : For the fame reafon , becaufe CBED is greater than a femicircle , the angles CAD , CED are equal : Therefore the whole angle BAD is equal to the C whole angle BED . Wherefore the angles in the fame fegment , & c . Q. E. D. ...
Side 88
... Firft , let the angles ABD , BAD , be equal to one another ; then the ftraight line BD is equal to DA , and therefore to DC ; and because the three ftraight lines DA , DB , DC are all equal , D is the centre of the cir- cled From the ...
... Firft , let the angles ABD , BAD , be equal to one another ; then the ftraight line BD is equal to DA , and therefore to DC ; and because the three ftraight lines DA , DB , DC are all equal , D is the centre of the cir- cled From the ...
Side 95
... Firft , Let the angle at C be a right angle , and bifect AB in F , and from the centre F , at the di- ftance FB , defcribe the femicircle AHB ; therefore the angle AHB in a femicircle is equal to the right angle at C. C H a 10.1 . A F ...
... Firft , Let the angle at C be a right angle , and bifect AB in F , and from the centre F , at the di- ftance FB , defcribe the femicircle AHB ; therefore the angle AHB in a femicircle is equal to the right angle at C. C H a 10.1 . A F ...
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The Elements of Euclid: Viz. The First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1793 |
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alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle bifected Book XI cafe centre circle ABCD circumference cone confequently conftruction cylinder defcribed demonftrated diameter drawn equal angles equiangular equimultiples Euclid excefs faid fame manner fame multiple fame ratio fame reafon fecond fegment fides BA fimilar fince firft firſt folid angle fome fore fphere fquare of AC ftraight line AB given angle given ftraight line given in fpecies given in magnitude given in pofition given magnitude given ratio gnomon greater join lefs leſs likewife line BC oppofite parallel parallelepipeds parallelogram perpendicular polygon prifm propofition proportionals pyramid Q. E. D. PROP rectangle contained rectilineal figure right angles ſquare thefe THEOR theſe triangle ABC vertex wherefore