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 9
... Solids; to which are Added, Elements of Plane and Spherical Trigonometry John Playfair. PROPOSITION I. THEOREM . If two triangles have two sides and the included angle in the one , equal to two sides and the included angle in the other ...
... Solids; to which are Added, Elements of Plane and Spherical Trigonometry John Playfair. PROPOSITION I. THEOREM . If two triangles have two sides and the included angle in the one , equal to two sides and the included angle in the other ...
Página 12
... Solids; to which are Added, Elements of Plane and Spherical Trigonometry John Playfair. being equal to the angle BGA , and the angle CAG equal to the angle CGA , by equal additions , the sum of the two angles BAG , CAG , is equal to the ...
... Solids; to which are Added, Elements of Plane and Spherical Trigonometry John Playfair. being equal to the angle BGA , and the angle CAG equal to the angle CGA , by equal additions , the sum of the two angles BAG , CAG , is equal to the ...
Página 13
... Solids; to which are Added, Elements of Plane and Spherical Trigonometry John Playfair. A For if BD be not in the same straight line with CB , let BE be in the same straight line with it ; therefore , because the straight line AB makes ...
... Solids; to which are Added, Elements of Plane and Spherical Trigonometry John Playfair. A For if BD be not in the same straight line with CB , let BE be in the same straight line with it ; therefore , because the straight line AB makes ...
Página 15
... Solids; to which are Added, Elements of Plane and Spherical Trigonometry John Playfair. AB ; the angle ABC is also greater than the angle BCA . A D Make AD equal to AB , and join BD : and because ADB is the exterior angle of the triangle ...
... Solids; to which are Added, Elements of Plane and Spherical Trigonometry John Playfair. AB ; the angle ABC is also greater than the angle BCA . A D Make AD equal to AB , and join BD : and because ADB is the exterior angle of the triangle ...
Página 18
... Solids; to which are Added, Elements of Plane and Spherical Trigonometry John Playfair. PROP . XVII . THEOR . A perpendicular is the shortest line that can be drawn from a point , situated with- out a straight line , to that line : any ...
... Solids; to which are Added, Elements of Plane and Spherical Trigonometry John Playfair. PROP . XVII . THEOR . A perpendicular is the shortest line that can be drawn from a point , situated with- out a straight line , to that line : any ...
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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