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 15
AB ; the angle ABC is also greater than the angle BCA . 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 interior and opposite angle DCB ; but ADB is equal ...
AB ; the angle ABC is also greater than the angle BCA . 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 interior and opposite angle DCB ; but ADB is equal ...
Página 16
Let the two straight lines BD , CD be drawn from B , C , the ends of the side BC of the triangle ABC , to the point D within it ; BD and DC are less than the other two sides BA , AC of the triangle , but contain an angle BDC greater ...
Let the two straight lines BD , CD be drawn from B , C , the ends of the side BC of the triangle ABC , to the point D within it ; BD and DC are less than the other two sides BA , AC of the triangle , but contain an angle BDC greater ...
Página 18
For , the angle ABC being a right one , the angle ACB is acute , ( Th . 10. ) or less than the angle ABC . But the less angle of a triangle is subtended by the less side ( Th . 12. ) ; therefore , the side AB is less than the side AC .
For , the angle ABC being a right one , the angle ACB is acute , ( Th . 10. ) or less than the angle ABC . But the less angle of a triangle is subtended by the less side ( Th . 12. ) ; therefore , the side AB is less than the side AC .
Página 19
... B therefore it is impossible that HCE D BC can differ from EF : hence , then , the triangles ABC and DEF are equal ... and meet towards B , D in the point G ; therefore GEF is a triangle , and its exterior angle AEF is greater ( 9.
... B therefore it is impossible that HCE D BC can differ from EF : hence , then , the triangles ABC and DEF are equal ... and meet towards B , D in the point G ; therefore GEF is a triangle , and its exterior angle AEF is greater ( 9.
Página 22
If a side of any triangle be produced , the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every trian- gle are equal to two right angles . Let ABC be a triangle , and let one of its ...
If a side of any triangle be produced , the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every trian- gle are equal to two right angles . Let ABC be a triangle , and let one of its ...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Vista de fragmentos - 1836 |
Términos y frases comunes
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 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 spherical 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 |
| Edición | 6 |
| Editor | W.E. Dean, 1836 |
| Largo | 311 páginas |
| Exportar cita | BiBTeX EndNote RefMan |