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 Trigonometry |
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Page 24
... join FC , GB . Because AF is equal to AG , and AB to AC , the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG common to the two trian- gles , AFC , AGB ; therefore the base FC is equal ( 4 ...
... join FC , GB . Because AF is equal to AG , and AB to AC , the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG common to the two trian- gles , AFC , AGB ; therefore the base FC is equal ( 4 ...
Page 25
... join DC ; therefore , be- cause 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 ...
... join DC ; therefore , be- cause 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 ...
Page 26
... Join CD , and if possible let CB be equal to DB ; then , in the case in which the vertex of each of the triangles is without the other trian- gle , because AC is equal to AD , the angle ACD is equal ( 5. 1. ) to the angle ADC : But the ...
... Join CD , and if possible let CB be equal to DB ; then , in the case in which the vertex of each of the triangles is without the other trian- gle , because AC is equal to AD , the angle ACD is equal ( 5. 1. ) to the angle ADC : But the ...
Page 27
... join DE , and upon it describe ( 1. 1. ) an equilateral 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 ...
... join DE , and upon it describe ( 1. 1. ) an equilateral 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 ...
Page 28
... join FC ; the straight line FC , drawn from the given point C , is at right angles to the given straight line AB , ADC EB Because DC is equal to CE , and FC common to the two tri- angles DCF , ECF , the two sides DC , CF are equal to ...
... join FC ; the straight line FC , drawn from the given point C , is at right angles to the given straight line AB , ADC EB Because DC is equal to CE , and FC common to the two tri- angles DCF , ECF , the two sides DC , CF are equal to ...
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Common terms and phrases
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 MDCCCXX meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals 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 straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore