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 1
Every definition ought to be clear , and expressed in words that are common and perfectly well understood . 4. An Axiom , or Maxim , is a self - evident proposition , requiring no formal demonstration to prove the truth of it ; but is ...
Every definition ought to be clear , and expressed in words that are common and perfectly well understood . 4. An Axiom , or Maxim , is a self - evident proposition , requiring no formal demonstration to prove the truth of it ; but is ...
Página 4
... can two 66 straight lines have a common segment ; that is , they cannot coincide " in part , without coinciding altogether . " 4. A superficies is that which has only length and breadth . " COR . The extremities of a superficies are ...
... can two 66 straight lines have a common segment ; that is , they cannot coincide " in part , without coinciding altogether . " 4. A superficies is that which has only length and breadth . " COR . The extremities of a superficies are ...
Página 10
... and the side CD common ; therefore , these two triangles are identical , or equal in all respects , ( Theor . 1. ) ; and conse- quently , the angle A equal to the angle B. A COR . Every equilateral triangle is also equiangular .
... and the side CD common ; therefore , these two triangles are identical , or equal in all respects , ( Theor . 1. ) ; and conse- quently , the angle A equal to the angle B. A COR . Every equilateral triangle is also equiangular .
Página 11
... one of them is greater than the other : Let AB be the greater , and from it cut off DB equal to AC the less , and join DC ; therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides ...
... one of them is greater than the other : Let AB be the greater , and from it cut off DB equal to AC the less , and join DC ; therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides ...
Página 13
... but the angles ABC , ABD are likewise together equal to two right an- gles : therefore the angles CBA , ABE are equal to the angles CBA , ABD : Take away the common angle ABC , and the remaining angle ABE is equal ( 3.
... but the angles ABC , ABD are likewise together equal to two right an- gles : therefore the angles CBA , ABE are equal to the angles CBA , ABD : Take away the common angle ABC , and the remaining angle ABE is equal ( 3.
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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 |