## Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement of the Quadrature of the Circle and the Geometry of Solids |

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Página 131

V. If there be four magnitudes , and if any

V. If there be four magnitudes , and if any

**equimultiples**what- See N. soever be taken of the first and third , and any**equimultiples**whatsoever of the second and fourth , and if , according as the multiple of the first is greater than ... Página 135

I.

I.

**EQUIMULTIPLES**of the same , or of equal magnitudes , are equal to one another . II . Those magnitudes of which the same , or equal , magnitudes are**equimultiples**, are equal to one another . III . A multiple of a greater magnitude is ... Página 136

IF any number of magnitudes be

IF any number of magnitudes be

**equimultiples**of as many others , each of each , what multiple soever any one of the first is of its part , the same multiple is the sum of all the first of the sum of all the rest . > a Ax 2. 1 . Página 137

IF the first of four magnitudes have the same ratio to the second which the third has to the fourth , and if any

IF the first of four magnitudes have the same 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 ... Página 138

Take of mA and mC

Take of mA and mC

**equimultiples**by any number p , and of nB and nD**equimultiples**by any number 9. The**equimultiples**of mA and mC by p are**equimultiples**also of A and C , for they contain A and C as often as there are units a 3.### Comentarios de la gente - Escribir un comentario

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### Términos y frases comunes

ABC is equal ABCD altitude angle ABC angle ACB angle BAC arch base bisected Book centre circle circle ABC circumference coincide common compounded contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equilateral equimultiples extremities fall figure fore four fourth given straight line greater half inscribed interior join less Let ABC line AC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism PROB produced PROP proportional proposition proved pyramid Q. E. D. PROP ratio reason rectangle contained rectilineal figure right angles segment shown sides similar solid square taken THEOR third triangle ABC wherefore whole

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Página 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...

Página 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.

Página 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.

Página 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.

Página 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.

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

Página 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.

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

Página 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.

Página 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.