Elements of Geometry: Being Chiefly a Selection from Playfair's GeometryA. Walker, 1829 - 186 páginas |
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Página 158
... cone is described . 13. The base of a cone is the circle about which the des- cribing line revolves . 14. A cylinder is a solid figure described by the revolution of a rectangle about one of its sides , which remains fixed . 15. The ...
... cone is described . 13. The base of a cone is the circle about which the des- cribing line revolves . 14. A cylinder is a solid figure described by the revolution of a rectangle about one of its sides , which remains fixed . 15. The ...
Página 167
... cone be cut by a plane parallel to its base , the section will be a circle ; and the section and the base will be to each other as the squares of their distances from the vertex of the cone . Let ABCD be a cone , and EFG a section ...
... cone be cut by a plane parallel to its base , the section will be a circle ; and the section and the base will be to each other as the squares of their distances from the vertex of the cone . Let ABCD be a cone , and EFG a section ...
Página 168
... cone , and meet EFG in the points O , F , G. Because the planes DHB , DHC cut the parallel planes EFG , ABC , the section OF is parallel to HB , and the section OG to HC ( 11.11 ) . Since OF is parallel to HB , the angle DOF is equal to ...
... cone , and meet EFG in the points O , F , G. Because the planes DHB , DHC cut the parallel planes EFG , ABC , the section OF is parallel to HB , and the section OG to HC ( 11.11 ) . Since OF is parallel to HB , the angle DOF is equal to ...
Página 169
... cones of equal bases and altitudes are equal to one another . Let the pyramid ABCD and the cone KLMS stand on equal bases ABC , KLMN , and have equal altitudes DH , ST ; the pyramid is equal to the cone . Let the sections EFG , PQR , be ...
... cones of equal bases and altitudes are equal to one another . Let the pyramid ABCD and the cone KLMS stand on equal bases ABC , KLMN , and have equal altitudes DH , ST ; the pyramid is equal to the cone . Let the sections EFG , PQR , be ...
Página 170
... cone are equal to each other . But the two solids are supposed to consist of an indef- inite number of equal and parallel sections or plates ; therefore they are equal . Therefore , pyramids & c Q. E. D. Cor . If a pyramid and a cone of ...
... cone are equal to each other . But the two solids are supposed to consist of an indef- inite number of equal and parallel sections or plates ; therefore they are equal . Therefore , pyramids & c Q. E. D. Cor . If a pyramid and a cone of ...
Otras ediciones - Ver todas
Elements of Geometry: Being Chiefly a Selection From Playfair's Geometry John Playfair Sin vista previa disponible - 2023 |
Elements of Geometry: Being Chiefly a Selection From Playfair's Geometry John Playfair Sin vista previa disponible - 2023 |
Términos y frases comunes
ABC is equal ABCD alternate angles angle ABC angle ACB angle BAC angles AGH angles equal base ABC bases and altitudes bisect centre chord circumference cone Consequently cylinder demonstrations described diagonals diameter divided draw equal angles equal arches equal bases equal circles equal to AC equiangular Euclid's Euclid's Elements exterior angle fore four quantities four right angles geometry given point given straight line gles greater Hence homologous sides intersect KLMN Let ABC meet opposite angles opposite side paral parallel lines parallel to CD parallelogram parallelopipeds perp perpendicular plane polygon prism Prop pyramid Q. E. D. COR Q. E. D. PROPOSITION radius rectangle contained right angled triangle Scholium segments semicircle side AC similar similar triangles solid square straight line &c subtended tangent THEOREM triangle ABC vertex wherefore
Pasajes populares
Página 36 - Any two sides of a triangle are together greater than the third side.
Página 80 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Página 42 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line...
Página 30 - To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line : it is required to divide it intotwo equal parts.
Página 20 - LET it be granted that a straight line may be drawn from any one point to any other point.
Página 38 - Problem. At a given point in a given straight line to make a rectilineal angle equal to a given rectilineal angle.
Página 113 - Wherefore also the angle BAD is equal to the angle CAD : Therefore the angle BAC is cut into two equal angles by the straight line AD.
Página 24 - DE ; the point B shall coincide with the point E, because AB is equal to DE; and AB coinciding with DE, AC shall coincide...
Página 36 - The greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it.