## The Elements of Euclid, containing the first six books, with a selection of geometrical problems. To which is added the parts of the eleventh and twelfth books which are usually read at the universities. By J. Martin1874 |

### Dentro del libro

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Página 59

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**square**upon a given straight line . Let AB be the given straight line . It is required to describe a**square**upon AB . D B Construction . From the point A draw**AC**at right angles to AB ( I. 11 ) ; make AD equal to AB ( I. 3 ) ; through ... Página 61

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**squares**described upon BA ,**AC**. F H K D Construction . On BC describe the**square**BDEC ( I. 46 ) ; and on BA ,**AC**, the**squares**GB , HC ; through A draw AL parallel to BD or CE ( I. 31 ) , and join AD , FC . Demonstration . Then because ... Página 62

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**square**GB is double of the triangle FBC , because these also are upon the same base FB , and between the same ...**AC**; therefore 10. The**square**upon the side BC is equal to the**squares**upon the sides AB ,**AC**. Therefore , in any right ... Página 63

... square on AB , to each of these equals add the

... square on AB , to each of these equals add the

**square on AC**; therefore but 2. The squares on AD , AC are equal to the squares on AB , AC ; 3. The squares on AD , AC are equal to the square on DC ( I. 47 ) , because the angle DAC is a ... Página 66

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**square**on AB . B D Construction . Upon AB describe the**square**ADEB ( I. 46 ) , and through C draw CF parallel to AD ...**AC**; for it is contained by DA ,**AC**; of which DA is equal to AB ; and 2. CE is contained by AB , BC ; for BE is ...### Otras ediciones - Ver todas

The Elements of Euclid, Containing the First Six Books, with a Selection of ... Euclides Sin vista previa disponible - 2016 |

### Términos y frases comunes

AC is equal adjacent angles angle ABC angle ACB angle BAC angle BCD angle DEF angle EDF angle equal base BC bisected centre circle ABC circumference constr Demonstration diameter double equal angles equal to F equiangular equilateral triangle equimultiples ex æquali exterior angle fourth given circle given point given straight line gnomon greater ratio inscribed less Let ABC Let the straight linear units meet multiple opposite angle parallel to BC parallelogram perpendicular plane polygon produced proportionals Q.E.D. PROPOSITION quadrilateral rectangle contained remaining angle right angles segment semicircle similar square on AC straight line AB straight line BC straight line drawn three straight lines tiple touches the circle triangle ABC triangle DEF twice the rectangle wherefore

### Pasajes populares

Página 1 - 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 6 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...

Página 232 - If two triangles, which have two sides of the one proportional to two sides of the other, be joined at one angle, so as to have their homologous sides parallel to one another, the remaining sides shall be in a straight line. Let...

Página 112 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.

Página 209 - ... triangles which have one angle in the one equal to one angle in the other, and their sides about the equal angles reciprocally proportional, are equal to one another.

Página 269 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.

Página 199 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Página 23 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.

Página 63 - If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section. Let the straight line AB be divided into two equal parts...

Página 32 - ... twice as many right angles as the figure has sides ; therefore all the angles of the figure together with four right angles, are equal to twice as many right angles as the figure has sides.