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 12
... 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 sum of the two angles BGA , CGA , ( Ax ...
... 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 sum of the two angles BGA , CGA , ( Ax ...
Página 15
... 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 BDC , it is greater ( 9. 1. ) than the ...
... 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 BDC , it is greater ( 9. 1. ) than the ...
Página 18
... 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 two oblique lines drawn from the samę ...
... 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 two oblique lines drawn from the samę ...
Página 19
... Plane and Spherical Trigonometry John Playfair. for the right angles B and E are equal , the side AB = DE , and BH = EF ; hence , these tri- angles are equal ( Th . 1. ) , and consequently AH = DF . Now ( by hyp . ) , we have DF - AC ...
... Plane and Spherical Trigonometry John Playfair. for the right angles B and E are equal , the side AB = DE , and BH = EF ; hence , these tri- angles are equal ( Th . 1. ) , and consequently AH = DF . Now ( by hyp . ) , we have DF - AC ...
Página 26
... Plane and Spherical Trigonometry John Playfair. C B D Because AB is parallel to CD , and BC meets them , the alternate angles ABC , BCD are equal ( 21. 1. ) to one another ; and because AC is parallel to BD , and BC meets them , the ...
... Plane and Spherical Trigonometry John Playfair. C B D Because AB is parallel to CD , and BC meets them , the alternate angles ABC , BCD are equal ( 21. 1. ) to one another ; and because AC is parallel to BD , and BC meets them , the ...
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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