## 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 5

Of four sided figures , a

Of four sided figures , a

**square**is that which has all its sides equal , and all its angles right angles . XXVI . An oblong is that which has all its angles right angles , but has not all its sides equal . XXVII . Página 45

TO describe a

TO describe a

**square**upon a given straight line . Let AB be the given straight line ; it is required to describe a**square**upon AB . From the point A drawa AC at right angles to AB , and a 11. 1 . makeb AD equal to AB , and through the ... Página 46

Book I. Let ABC be a right angled triangle having the right angle BAC ; the

Book I. Let ABC be a right angled triangle having the right angle BAC ; the

**square**described upon the side BC is equal to the squares described upon BA , AC . a 46. 1 . On BC describea the**square**BDEC , and on BA , AC the b 31. Página 47

Book I. IF the

Book I. IF the

**square**described upon one of the sides of a triangle be equal to the squares described upon the other two sides of it , the angle contained by these two sides is a right angle . D. If the**square**described upon BC , one of ... Página 49

Also , instead of the

Also , instead of the

**square**of a line , as AD , we n . may sometimes write AD . " “ The sign + placed between the names of two magnitudes , signifies that those magnitudes are to be added together ; " and the sign - placed between them ...### 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.