Elements of Geometry; Containing the First Six Books of Euclid ...For Bell & Bradfute, 1814 - 461 Seiten |
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Seite 28
... join DC ; therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; but the angle DBC is also equal to the angle ACB ; therefore the ...
... join DC ; therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; but the angle DBC is also equal to the angle ACB ; therefore the ...
Seite 29
... Join CD , and if possible let CB be equal to DB ; then , in the case in which the ver- tex of each of the triangles is without the other triangle , because AC is equal to AD , the angle ACD is equal a to the angle ADC : But the A D ...
... Join CD , and if possible let CB be equal to DB ; then , in the case in which the ver- tex of each of the triangles is without the other triangle , because AC is equal to AD , the angle ACD is equal a to the angle ADC : But the A D ...
Seite 31
... join DE , and upon it describe an equilate- ral triangle DEF ; then join AF ; the straight line AF bi- sects the angle BAC . ; Because AD is equal to AE , and AF is common to the two triangles DAF , EAF the two sides DA , AF , are equal ...
... join DE , and upon it describe an equilate- ral triangle DEF ; then join AF ; the straight line AF bi- sects the angle BAC . ; Because AD is equal to AE , and AF is common to the two triangles DAF , EAF the two sides DA , AF , are equal ...
Seite 32
... join FC ; the straight line FC , drawn from the gi- ven point C , is at right angles to the given straight line AB . Because DC is equal A D C C E B to CE , and FC common to the two triangles DCF , ECF , the two sides DC , CF are equal ...
... join FC ; the straight line FC , drawn from the gi- ven point C , is at right angles to the given straight line AB . Because DC is equal A D C C E B to CE , and FC common to the two triangles DCF , ECF , the two sides DC , CF are equal ...
Seite 36
... join BE and produce it to F , and make EF equal to BE ; join also FC , and produce AC to G. B E C D G Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the an- gle AEB is equal to the angle CEF ...
... join BE and produce it to F , and make EF equal to BE ; join also FC , and produce AC to G. B E C D G Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the an- gle AEB is equal to the angle CEF ...
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Häufige Begriffe und Wortgruppen
ABC is equal ABCD altitude angle ABC angle ACB angle BAC arch AC base BC bisected Book centre circle ABC circumference cosine cylinder definition demonstrated described diameter draw drawn equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles GEOMETRY given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet opposite angle parallel parallelogram perpendicular polygon prism PROB 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 parallelepipeds spherical angle spherical triangle SPHERICAL TRIGONOMETRY straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore