## Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement of the Quadrature of the Circle and the Geometry of SolidsF. Nichols, 1806 - 311 sider |

### Fra bogen

Resultater 6-10 af 16

Side 259

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**prism**and a parallelepiped , which have the same altitude , are to each other as their bases ; that is , the**prism**BNM is to the parallelepiped CD as the triangle AEM to the parallelogram LG . For , by the last corollary , the**prism**... Side 261

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**prisms**are to one another in the ratio compounded of the ratio of their bases , and of the ratio of their altitudes . For every**prism**is equal to a parallelepiped of the same altitude with it , and of an equal bases . g 2. Cor . 8. 3 ... Side 262

... , & c . Q. E. D. Cor . In the same manner it may be demonstrated that equal

... , & c . Q. E. D. Cor . In the same manner it may be demonstrated that equal

**prisms**have their bases and altitudes reciprocally pro- portional , and conversely . 1 PROP . XI . THEOR . gunmure / SIMILAR solid 262 ELEMENTS. Side 264

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**prisms**are to one another in the tri- plicate ratio , or in the ratio of the cubes , of their homologous sides . For a**prism**is equal to half of a parallelepiped of the 84. 3. Sup . same base and altitudes . / PROP . XII . THEOR . IF ... Side 266

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**prisms**hving all the same altitude may be circumscribed about the pramid ABCD , so that their sum shall exceed ABCD by solid less than Z. Let Z be qual to a**prism**standing on the same base BCD with the pyrmid , and having for its ...### Andre udgaver - Se alle

### Almindelige termer og sætninger

ABC is equal altitude angle ABC angle ACB angle BAC angle contained angle EDF arch base BC bisected Book centre circle ABC circumference coincide common section cylinder definition demonstrated diameter draw drawa equal angles equiangular equilateral polygon equimultiples Euclid exterior angle fore four right angles given circle given straight line greater inscribed interior and opposite join less Let ABC Let the straight meet multiple opposite angle parallelogram parallelogram ABCD perpendicular point F polygon prism PROB produced proportional proposition pyramid Q. E. D. COR Q. E. D. PROP ratio rectangle contained rectilineal figure remaining angle segment solid angle solid parallelepipeds straight line AB straight line AC Suppl THEOR third touches the circle triangle ABC triangle DEF

### Populære passager

Side 121 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...

Side 42 - TO a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

Side 63 - Therefore, in obtuse-angled triangles, &c. QED PROP. XIII. THEOREM. In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.

Side 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.

Side 183 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let AC, CF be equiangular parallelograms having the angle BCD equal to the angle ECG ; the ratio of the parallelogram AC to the parallelogram CF is the same with the ratio which is compounded •f the ratios of their sides.

Side 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.

Side 291 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 160 - ... extremities of the base shall have the same ratio which the other sides of the triangle have to one...

Side 10 - ... shall be greater than the base of the other. Let ABC, DEF be two triangles, which have the two sides AB, AC, equal to the two DE, DF, each to each, viz.

Side 14 - Therefore, upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extretnity equal to one another.