Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids ; to which are Added, Elements of Plane and Spherical TrigonometryW.E. Dean, 1839 - 318 páginas |
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Página 48
... angle CEF equal to D ; and through A draw ( 31. 1. ) AG parallel to BC , and through C draw CG ( 31. 1. ) parallel ... remaining complement BK is equal to the remaining comple- ment KD . Wherefore , the complements , & c . Q. E. D. ...
... angle CEF equal to D ; and through A draw ( 31. 1. ) AG parallel to BC , and through C draw CG ( 31. 1. ) parallel ... remaining complement BK is equal to the remaining comple- ment KD . Wherefore , the complements , & c . Q. E. D. ...
Página 59
... angle ; and therefore the whole AEB is a right angle ; And because the angle GEF is half a right angle , and EGF a right angle , for it is equal ( 29. 1. ) to the interior and opposite F G angle ECB , the remaining angle EFG A C DB is half ...
... angle ; and therefore the whole AEB is a right angle ; And because the angle GEF is half a right angle , and EGF a right angle , for it is equal ( 29. 1. ) to the interior and opposite F G angle ECB , the remaining angle EFG A C DB is half ...
Página 60
... angle CEA is equal ( 5. 1. ) to the angle EAC ; and the an- gle ACE is a right angle ; therefore each of the angles ... remaining angle DGB is half a right angle , and is therefore equal to the angle DBG ; wherefore also the side ...
... angle CEA is equal ( 5. 1. ) to the angle EAC ; and the an- gle ACE is a right angle ; therefore each of the angles ... remaining angle DGB is half a right angle , and is therefore equal to the angle DBG ; wherefore also the side ...
Página 61
... angle EAB is a right angle ; therefore the rectangle CF.FA , together with the square of AE , is equal to the squares of BA , AE : take away the square of AE , which is common to both , therefore the remaining rectangle CF. FA is ...
... angle EAB is a right angle ; therefore the rectangle CF.FA , together with the square of AE , is equal to the squares of BA , AE : take away the square of AE , which is common to both , therefore the remaining rectangle CF. FA is ...
Página 63
... angle , the angle ACB is greater ( 16. 1. ) than a right angle , and AB = ( 12. 2. ) AC + BC2 + 2BC.CD . Add BC to ... remaining rectangle BE . EF is equal to the square of EH : But BD is the rectangle con- A H B F G E C D See ...
... angle , the angle ACB is greater ( 16. 1. ) than a right angle , and AB = ( 12. 2. ) AC + BC2 + 2BC.CD . Add BC to ... remaining rectangle BE . EF is equal to the square of EH : But BD is the rectangle con- A H B F G E C D See ...
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Términos y frases comunes
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder definition demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet opposite angle parallel parallelogram parallelopipeds perpendicular polygon prism produced proportional proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelopipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore