## 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 56

Side 130

... when the greater contains the less a certain number of times exactly . III .

... when the greater contains the less a certain number of times exactly . III .

**Ratio**is a mutual relation of two magnitudes , of the same kind , to one another , in respect of quantity . Book V. IV . Magnitudes are said to be of 130 ELEMENTS. Side 131

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**ratio**to one another . V. If there be four magnitudes , and if any equimultiples what- See N. soever be taken of the ...**ratio**that the third has to the fourth . VI . Magnitudes are said to be proportionals , when the first has the same ... Side 132

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**ratio**which the first has to the second , and of the**ratio**which the second has to the third , and of the**ratio**which ...**ratio**of the first to the second . " Thus , if A be to B as B to C , the**ratio**of A to C is said to be duplicate of ... Side 133

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**ratio**of the first to the second ; and so on , according to the number of**ratios**. Hence , a**ratio**compounded of three equal**ratios**is triplicate of any one of those**ratios**; a**ratio**compounded of four equal**ratios**quadruplicate , " & c ... Side 137

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**ratio**to the second which the third has to the fourth , and if any equimultiples whatever be taken of the first and third , and any whatever of the second and fourth ; the multiple of the first will have the same**ratio**to the multiple ...### 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.