## 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

Side 190

A

parallelogram about one of its sides , which remains fixed . 15. The axis of a

bases of a ...

A

**cylinder**is a solid figure described by the revolution of a right angledparallelogram about one of its sides , which remains fixed . 15. The axis of a

**cylinder**is the fixed straight line about which the parallelogram revolves . 16. Thebases of a ...

Side 205

If from any point in the circumference of the base of a

drawn perpendicular to the plane of the base , it will be wholly in the cylindric

superficies . Let ABCD be a

...

If from any point in the circumference of the base of a

**cylinder**, a straight line bedrawn perpendicular to the plane of the base , it will be wholly in the cylindric

superficies . Let ABCD be a

**cylinder**of which the base is the circle AEB , DFC the...

Side 206

But A D is always in the superficies of the

superficies ; therefore , EF is also in the superficies of the

. THEOR . A

equal to ...

But A D is always in the superficies of the

**cylinder**, for it describes thatsuperficies ; therefore , EF is also in the superficies of the

**cylinder**. a PROP . XVII. THEOR . A

**cylinder**and a parallelopiped having equal bases and altitudes , areequal to ...

Side 207

The point R will fall between P and N. On the polygon AGKBLM let an upright

prism AGBCD be constituted of the same altitude with the

therefore be less than the

through ...

The point R will fall between P and N. On the polygon AGKBLM let an upright

prism AGBCD be constituted of the same altitude with the

**cylinder**, which willtherefore be less than the

**cylinder**, because it is within it ( 16. 3. Sup . ) ; and ifthrough ...

Side 208

Because the polygon BECFD is greater than the circle LIM , the prise BCFKHG is

greater than the

has the greater base . But the pyramid ABECFD is the third part of the prism ( 15.

Because the polygon BECFD is greater than the circle LIM , the prise BCFKHG is

greater than the

**cylinder**LMNO , for they have the same ' altitude , but the prismhas the greater base . But the pyramid ABECFD is the third part of the prism ( 15.

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Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Uten tilgangsbegrensning - 1819 |

Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Uten tilgangsbegrensning - 1854 |

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

### 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 spherical square straight line taken tangent THEOR third touch triangle ABC wherefore whole