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 31
... Plane and Spherical Trigonometry John Playfair. Now because the angle DBC is equal to the angle FBA , each of them being a right angle , adding to each the angle ABC , the whole angle DBA will be equal ( 2. Ax . ) to the whole FBC ; and ...
... Plane and Spherical Trigonometry John Playfair. Now because the angle DBC is equal to the angle FBA , each of them being a right angle , adding to each the angle ABC , the whole angle DBA will be equal ( 2. Ax . ) to the whole FBC ; and ...
Página 36
... Plane and Spherical Trigonometry John Playfair. G , at the distance GH , describe ( 3. Post . ) another circle HLK ; and join KF , KG ; the triangle KFG has its sides equal to the three straight lines , A , B , C. Because the point F is ...
... Plane and Spherical Trigonometry John Playfair. G , at the distance GH , describe ( 3. Post . ) another circle HLK ; and join KF , KG ; the triangle KFG has its sides equal to the three straight lines , A , B , C. Because the point F is ...
Página 41
... Plane and Spherical Trigonometry John Playfair. the parallels KM , FG , the alternate angles MHG , HGF are equal ( 21. 1. ) ; add to each of these the angle HGL ; therefore the angles MHG , HGĹ , are equal to the angles HGF , HGL : But ...
... Plane and Spherical Trigonometry John Playfair. the parallels KM , FG , the alternate angles MHG , HGF are equal ( 21. 1. ) ; add to each of these the angle HGL ; therefore the angles MHG , HGĹ , are equal to the angles HGF , HGL : But ...
Página 46
... Plane and Spherical Trigonometry John Playfair. PROP . III . THEOR . If a straight line be divided into any two parts , the rectangle contained by the whole and one of the parts , is equal to the rectangle contained by the two parts ...
... Plane and Spherical Trigonometry John Playfair. PROP . III . THEOR . If a straight line be divided into any two parts , the rectangle contained by the whole and one of the parts , is equal to the rectangle contained by the two parts ...
Página 54
... Plane and Spherical Trigonometry John Playfair. From A draw AE perpendicular to BC , and because BEA is a right angle , AB2 = ( 37 . 1. ) BE2 + AE2 and AC2 = CE2 + AE2 ; wherefore AB2 + AC2 - BE2 + CE2 + 2AE2 . But because the line BC is ...
... Plane and Spherical Trigonometry John Playfair. From A draw AE perpendicular to BC , and because BEA is a right angle , AB2 = ( 37 . 1. ) BE2 + AE2 and AC2 = CE2 + AE2 ; wherefore AB2 + AC2 - BE2 + CE2 + 2AE2 . But because the line BC is ...
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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