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

### Dentro del libro

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Página 131

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

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 132

... to the last of them the ratio compounded of the ratio which the first has to the second , and of the ratio which the second has to the third , and of the ratio which the third has to the

... to the last of them the ratio compounded of the ratio which the first has to the second , and of the ratio which the second has to the third , and of the ratio which the third has to the

**fourth**, and so on unto the last magnitude . Página 133

If four magnitudes are continual proportionals , the ratio of the first to the

If four magnitudes are continual proportionals , the ratio of the first to the

**fourth**is said to be triplicate of the ratio of the first to the second , or of the ratio of the second to the third , & c . “ So also , if there are five ... Página 134

Dividendo , by division : when there are four proportionals , and it is inferred , that the excess of the first above the second is to the second , as the excess of the third above the

Dividendo , by division : when there are four proportionals , and it is inferred , that the excess of the first above the second is to the second , as the excess of the third above the

**fourth**is to the**fourth**. 17th prop . book 5 . Página 135

and as the third is to the

and as the third is to the

**fourth**of the first rank , so is the Book V : third from the last to the last but two of the second rank ; and so on in a cross , or inverse , order ; and the inference is as in the 19th definition .### 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

### Pasajes populares

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.