## 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 |

### Inni boken

Resultat 1-5 av 11

Side 189

A

opposite are equal , similar , and parallel to one another ; and the others are

parallelograms . 5. A parallelopiped is a solid figure contained by six

quadrilateral figures ...

A

**prism**is a solid figure contained by plane figures , of which two that areopposite are equal , similar , and parallel to one another ; and the others are

parallelograms . 5. A parallelopiped is a solid figure contained by six

quadrilateral figures ...

Side 193

Therefore the

AB is cut into two equal

lines of a parallelopiped , mentioned in the following propositions , are the sides

of ...

Therefore the

**prism**CAE is equal to the**prism**CBE ( 1. 3. Sup . ) , and the solidAB is cut into two equal

**prisms**by the plane CDEF . N. B. , The insisting straightlines of a parallelopiped , mentioned in the following propositions , are the sides

of ...

Side 194

because that the parallel planes AD and LH , as also AE and LK н E K D E н K M

/ M N G B A Α . are cut by the same prane DN : therefore the

are equal ( 1. 3. Sup . ) . If therefore the

because that the parallel planes AD and LH , as also AE and LK н E K D E н K M

/ M N G B A Α . are cut by the same prane DN : therefore the

**prisms**DAG , HLNare equal ( 1. 3. Sup . ) . If therefore the

**prism**LNH be taken from the solid , of ... Side 197

From this it is manifest , that

altitude , are to one another as their bases . ... For by the last Cor . the

is to the

From this it is manifest , that

**prisms**upon triangular bases , and of the samealtitude , are to one another as their bases . ... For by the last Cor . the

**prism**BNMis to the

**prism**DPG as the triangle AME to the triangle CGF , and therefore the**prism**... Side 199

Cor . 3. Hence all

of their bases , and of their altitudes . For every

of the same altitude with it , and of an equal base ( 2. Cor . 8. 3. Sup . ) . PROP .

Cor . 3. Hence all

**prisms**are to one another in the ratio compounded of the ratiosof their bases , and of their altitudes . For every

**prism**is equal to a parallelopipedof the same altitude with it , and of an equal base ( 2. Cor . 8. 3. Sup . ) . PROP .

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Elements of Geometry: Containing the First Six Books of Euclid with a ... John Playfair Uten tilgangsbegrensning - 1855 |

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### Vanlige uttrykk og setninger

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