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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Página 13
to two right angles ; but the angles ABC , ABD are E likewise together equal to two right angles : therefore the angles ... If one side of a triangle be produced , the exterior angle is greater than either of the interior , and opposite ...
to two right angles ; but the angles ABC , ABD are E likewise together equal to two right angles : therefore the angles ... If one side of a triangle be produced , the exterior angle is greater than either of the interior , and opposite ...
Página 14
Produce BC to D ; and because ACD is the exterior angle of the triangle ABC , ACD is greater ( 9. 1. ) than the interior and opposite angle А ABC ; to each of these add the angle ACB ; therefore the angles ACD , ACB are greater than the ...
Produce BC to D ; and because ACD is the exterior angle of the triangle ABC , ACD is greater ( 9. 1. ) than the interior and opposite angle А ABC ; to each of these add the angle ACB ; therefore the angles ACD , ACB are greater than the ...
Página 15
AB ; the angle ABC is also greater than the angle BCA . A Make AD equal to AB , and join BD : and because ADB is the exterior angle of the triangle BDC , it is greater ( 9. 1. ) .D than the interior and opposite angle DCB ; but ADB is ...
AB ; the angle ABC is also greater than the angle BCA . A Make AD equal to AB , and join BD : and because ADB is the exterior angle of the triangle BDC , it is greater ( 9. 1. ) .D than the interior and opposite angle DCB ; but ADB is ...
Página 16
Again , because the exterior angle of a triangle ( 9. 1. ) is greater than the interior and opposite angle , the exterior angle BDC of the triangle CDE is greater than CED ; for the same reason , the exterior angle CEB of the triangle ...
Again , because the exterior angle of a triangle ( 9. 1. ) is greater than the interior and opposite angle , the exterior angle BDC of the triangle CDE is greater than CED ; for the same reason , the exterior angle CEB of the triangle ...
Página 19
for the right angles B and E are equal , the side AB = DE , A D and BH = EF ; hence , these triangles are equal ( Th . 1. ) ... If a straight line falling upon two other straight lines makes the exterior angle equal to the interior and ...
for the right angles B and E are equal , the side AB = DE , A D and BH = EF ; hence , these triangles are equal ( Th . 1. ) ... If a straight line falling upon two other straight lines makes the exterior angle equal to the interior and ...
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ABCD altitude angle ABC angle BAC base bisected Book called centre chord circle circumference coincide common consequently construction cosine cylinder definition demonstrated described diameter difference distance divided double draw drawn equal equal angles equiangular equilateral Euclid exterior angle extremities fall fore four fourth given given straight line greater half Hence inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism Prob produced PROP proportional proposition proved radius ratio reason rectangle contained rectilineal figure remaining right angles segment shewn sides similar sine solid square straight line taken tangent THEOR third touch triangle ABC wherefore whole
Información bibliográfica
| Título | 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 |
| Autor | John Playfair |
| Editor | W. E. Dean, 1836 |
| Largo | 311 páginas |
| Exportar cita | BiBTeX EndNote RefMan |