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 10
If the triangle ABC have the side AC equal to the side BC : then will the angle B be equal to the angle A. For , conceive the angle C to be bisected , or divided into two equal parts by the line CD , making the angle ACD equal to the ...
If the triangle ABC have the side AC equal to the side BC : then will the angle B be equal to the angle A. For , conceive the angle C to be bisected , or divided into two equal parts by the line CD , making the angle ACD equal to the ...
Página 23
For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides , by drawing straight lines from a point F within the figure to each of its angles . And , by the preceding proposition , all the angles of ...
For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides , by drawing straight lines from a point F within the figure to each of its angles . And , by the preceding proposition , all the angles of ...
Página 24
And , by joining BD , BE , BF , the figure is divided into four triangles , which contain eight right angles ; that is , as many times two right angles as there are units in the number of sides diminished by two .
And , by joining BD , BE , BF , the figure is divided into four triangles , which contain eight right angles ; that is , as many times two right angles as there are units in the number of sides diminished by two .
Página 33
By the same construction , each of the halves BAF , CAF , may be divided into two equal parts ; and thus , by successive subdivisions , a given angle may be divided into four equal parts , into eight , into sixteen , and so on .
By the same construction , each of the halves BAF , CAF , may be divided into two equal parts ; and thus , by successive subdivisions , a given angle may be divided into four equal parts , into eight , into sixteen , and so on .
Página 34
DB , and the straight line AB is divided into two equal parts in the A B point D. D PROP . VI . PROB . To draw a straight line at right angles to a given straight line , from a given point in that line .
DB , and the straight line AB is divided into two equal parts in the A B point D. D PROP . VI . PROB . To draw a straight line at right angles to a given straight line , from a given point in that line .
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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 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 |
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