## 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 132

When three magnitudes are continual proportionals , the second is said to be a mean

When three magnitudes are continual proportionals , the second is said to be a mean

**proportional**between the other two . X. N. When there is any number of magnitudes of the same kind , the first is said to have to the last of them the ... Página 155

SIMILAR rectilineal figures are those which have their several angles equal , each to each , and the sides about the equal angles

SIMILAR rectilineal figures are those which have their several angles equal , each to each , and the sides about the equal angles

**proportional**. II . Two sides of one figure are said to be reciprocally**proportional**to two sides of ... Página 157

IF a straight line be drawn parallel to one of the sides of a triangle , it will cut the other sides , or the other sides produced

IF a straight line be drawn parallel to one of the sides of a triangle , it will cut the other sides , or the other sides produced

**proportionally**; and if the sides , or the sides produced , be cut**proportionally**, the straight line ... Página 158

A E D A ABA D В B4 D E B С > Next , let the sides AB , AC of the triangle ABC , or these sides produced , be cut

A E D A ABA D В B4 D E B С > Next , let the sides AB , AC of the triangle ABC , or these sides produced , be cut

**proportionally**in the points D , E , that is , so that BD be to DA , as CE to EA ; and join DE ; DE is parallel to BC . Página 161

THE sides about the equal angles of equiangular triangles are

THE sides about the equal angles of equiangular triangles are

**proportional**; and those which are opposite to the equal angles are homologous sides , that is , are the antecedents or consequents of the ratios .### 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.