Elements of Geometry: Being Chiefly a Selection from Playfair's GeometryA. Walker, 1829 - 186 páginas |
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Página 157
... prism or pyramid ; if a square , it is call- ed a square prism or pyramid . ED . 5. A parallelopiped is a prism , or solid figure , contained by six quadrilateral figures , whereof every opposite two are pa- rallel . 6. A cube is a ...
... prism or pyramid ; if a square , it is call- ed a square prism or pyramid . ED . 5. A parallelopiped is a prism , or solid figure , contained by six quadrilateral figures , whereof every opposite two are pa- rallel . 6. A cube is a ...
Página 160
... prism CAE is equal to the prism CBE ( 1. 12 ) , and the solid AB is divided into two equal prisms by the plane CDEF . There- fore , if a solid & c . Q. E. D. PROPOSITION IV . THEOREM . If a prism be cut 160 ELEMENTS OF.
... prism CAE is equal to the prism CBE ( 1. 12 ) , and the solid AB is divided into two equal prisms by the plane CDEF . There- fore , if a solid & c . Q. E. D. PROPOSITION IV . THEOREM . If a prism be cut 160 ELEMENTS OF.
Página 161
... prism be cut by a plane parallel to the base the section will be equal and like to the base Let LB be a prism , of which the base is ABCDE , and a section parallel to the base is IGHFK ; the section is equal to and like the base . Draw ...
... prism be cut by a plane parallel to the base the section will be equal and like to the base Let LB be a prism , of which the base is ABCDE , and a section parallel to the base is IGHFK ; the section is equal to and like the base . Draw ...
Página 162
... prisms , and GB a cylinder , having equal bases ABC , and equal altitudes ; the two prisms are equal to each other and to the cylinder . L H G L D E H I C B B A A B Suppose the prisms and cylinder to stand on the same plane , and be cut ...
... prisms , and GB a cylinder , having equal bases ABC , and equal altitudes ; the two prisms are equal to each other and to the cylinder . L H G L D E H I C B B A A B Suppose the prisms and cylinder to stand on the same plane , and be cut ...
Página 163
... prisms is equal to the corresponding section of the cylinder . Now if we consider these parallel sections as plates ... prisms & c . Q. E. D. See Note . COR . Rectangular parallelopipeds of equal bases and alti- tudes are equal to one ...
... prisms is equal to the corresponding section of the cylinder . Now if we consider these parallel sections as plates ... prisms & c . Q. E. D. See Note . COR . Rectangular parallelopipeds of equal bases and alti- tudes are equal to one ...
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.