## 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 1-5 af 36

Side 42

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**passes**, and let BK , KD be the other paral- lelograms , which make up the whole figure ABCD , and are therefore called the comple- ments . The complement BK is equal to the complement KD . Because ABCD is a paral- lelogram , and AC its ... Side 72

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**pass**through the centre , it will cut that line at right angles ; and if it cut it at right angles , it will bisect it . a 1. 3 . Let ABC be a circle , and let CD , a straight line drawn through the centre , bisect any straight line AB ... Side 73

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**pass**through the centre , they do not bisect each other . Let ABCD be a circle , and AC , BD two straight lines in it , which cut each other in the point E , and do not both**pass**through the centre ; AC , BD do not bisect each other ... Side 74

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**pass**through the centre , it must cut it at right angles ; wherefore FEA is a right angle . Again , because the straight line FE bisects the straight line BD , which does not**pass**through the centre , it must cut it at right angles ... Side 76

... ; that is , a line nearer to that which

... ; that is , a line nearer to that which

**passes**through the centre is equal to one which is more re- mote , which is impossible . Therefore , if any point be taken , & c . Q. E. D. PROP . VIII . THEOR . IF any point be 76 ELEMENTS.### Andre udgaver - Se alle

### Almindelige termer og sætninger

ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle contained angle EDF arch base BC bisected Book centre circle ABC circumference coincide 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 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.