## 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 8

... equal to BA : but it has been proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB ; but things which are equal to the same are d 1. Axi- equal to one anotherd ; therefore CA is equal to CB ;

... equal to BA : but it has been proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB ; but things which are equal to the same are d 1. Axi- equal to one anotherd ; therefore CA is equal to CB ;

**wherefore**CA ... Página 9

Def . to the remainders BG : but it has been shown , that BC is g 3. Ax . equal to BG ;

Def . to the remainders BG : but it has been shown , that BC is g 3. Ax . equal to BG ;

**wherefore**AL and BC are each of them equal to BG ; therefore the straight line AL is equal to BCh . h 1. Página 10

... AC shall coincide with DF , because the angle BAC is equal to the angle EDF ;

... AC shall coincide with DF , because the angle BAC is equal to the angle EDF ;

**wherefore**also the point C shall coincide ' with the point F , because AC is equal to DF : but the point B coincides with the point E ;**wherefore**the base ... Página 11

BF , FC are equal to the two CG , GB , each to each ; but the angle BFC is equal to the angle CGB ;

BF , FC are equal to the two CG , GB , each to each ; but the angle BFC is equal to the angle CGB ;

**wherefore**the triangles BFC , CGB are equalb , and their remaining angles are equal , to which the equal sides are opposite ; therefore ... Página 13

... upon the other side of the base CD , are equala to one another ; but the angle ĒCD is greater than the angle BCD ;

... upon the other side of the base CD , are equala to one another ; but the angle ĒCD is greater than the angle BCD ;

**wherefore**the angle FDC is likewise greater than BCD ; much more then is the angle BDC greater than the angle BCD .### 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.