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 189
A prism is a solid figure contained by plane figures , of which two that are opposite are equal , similar , and parallel to one another ; and the others are parallelograms . 5. A parallelopiped is a solid figure contained by six ...
A prism is a solid figure contained by plane figures , of which two that are opposite are equal , similar , and parallel to one another ; and the others are parallelograms . 5. A parallelopiped is a solid figure contained by six ...
Página 193
Therefore the prism CAE is equal to the prism CBE ( 1. 3. Sup . ) , and the solid AB is cut into two equal prisms by the plane CDEF . A D N. B. , The insisting straight lines of a parallelopiped , mentioned in the following propositions ...
Therefore the prism CAE is equal to the prism CBE ( 1. 3. Sup . ) , and the solid AB is cut into two equal prisms by the plane CDEF . A D N. B. , The insisting straight lines of a parallelopiped , mentioned in the following propositions ...
Página 194
because that the parallel planes AD and LH , as also AE and LK H E B K D E H K M N G A are cut by the same piane DN therefore the prisms DAG , HLN are equal ( 1. 3. Sup . ) . If therefore the prism LNH be taken from the solid , of which ...
because that the parallel planes AD and LH , as also AE and LK H E B K D E H K M N G A are cut by the same piane DN therefore the prisms DAG , HLN are equal ( 1. 3. Sup . ) . If therefore the prism LNH be taken from the solid , of which ...
Página 199
Hence all prisms are to one another in the ratio compounded of the ratios of their bases , and of their altitudes . For every prism is equal to a parallelopiped of the same altitude with it , and of an equal base ( 2. Cor . 8. 3. Sup . ) ...
Hence all prisms are to one another in the ratio compounded of the ratios of their bases , and of their altitudes . For every prism is equal to a parallelopiped of the same altitude with it , and of an equal base ( 2. Cor . 8. 3. Sup . ) ...
Página 200
In the same manner , it may be demonstrated , that equal prisms have their bases and altitudes reciprocally proportional , and conversely . PROP . XI . THEOR . Similar solid parallelopipeds are to one another in the triplicate ratio of ...
In the same manner , it may be demonstrated , that equal prisms have their bases and altitudes reciprocally proportional , and conversely . PROP . XI . THEOR . Similar solid parallelopipeds are to one another in the triplicate ratio of ...
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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 |