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 TrigonometryB. & S. Collins; W. E. Dean, printer, 1836 - 311 páginas |
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Página 60
... Plane and Spherical Trigonometry John Playfair. C BE is equal to CE , and FE common to the triangles BEF , CEF , the two sides CE , EF are equal to the two CE , EF : but the angle BEF is greater than the angle CEF ; there- fore the base ...
... Plane and Spherical Trigonometry John Playfair. C BE is equal to CE , and FE common to the triangles BEF , CEF , the two sides CE , EF are equal to the two CE , EF : but the angle BEF is greater than the angle CEF ; there- fore the base ...
Página 62
... Plane and Spherical Trigonometry John Playfair. Let then , FA , FB , and FC be drawn ; then , because FA , FB meet AB at equal distances from the perpendicular , they are equal . For similar reasons FB , FC , are equal ; hence the points ...
... Plane and Spherical Trigonometry John Playfair. Let then , FA , FB , and FC be drawn ; then , because FA , FB meet AB at equal distances from the perpendicular , they are equal . For similar reasons FB , FC , are equal ; hence the points ...
Página 63
... Plane and Spherical Trigonometry John Playfair. be less than the sum of their radii , and the greater radius will be also less than the sum of the smaller and the distance between the centres . For , CD is less ( 13. 1. ) than CA + AD ...
... Plane and Spherical Trigonometry John Playfair. be less than the sum of their radii , and the greater radius will be also less than the sum of the smaller and the distance between the centres . For , CD is less ( 13. 1. ) than CA + AD ...
Página 73
... Plane and Spherical Trigonometry John Playfair. 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 ...
... Plane and Spherical Trigonometry John Playfair. 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 ...
Página 74
... Plane and Spherical Trigonometry John Playfair. equal to it and the angle at A is half the angle BGC , and the angle at D'half of the angle EHF ; therefore the angle at A is equal to the angle at D. PROP . XXVII . THEOR . In equal ...
... Plane and Spherical Trigonometry John Playfair. equal to it and the angle at A is half the angle BGC , and the angle at D'half of the angle EHF ; therefore the angle at A is equal to the angle at D. PROP . XXVII . THEOR . In equal ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore