## 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 |

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Página 161

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**equimultiples**whatsoever of the first and third being taken , and any**equimultiples**whatsoever of the second and fourth ; if the multiple of the first be less than that of the second , the multiple of the third is also less than that of ... Página 166

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**equimultiples**, these shall be**equimultiples**, the one of the second , and the other of the fourth . Let A the first be the same multiple of B the second , that C the third is of D the fourth ; and of A , U let**equimultiples**EF , GH be ... Página 170

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**equimultiples**of the two E , F , and let AG , CH taken from the first two be**equimultiples**of the same E , F. Then the remainders GB , HD shall be either**equal**to E , F , or**equi- multiples**of them . A K G B E F HD First . Let GB be**equal**... Página 172

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**equimultiples**; and that G is less than E , therefore Α G B E C H D F 2. His less than F ( V. Def . 5 ) ; that is ...**equimultiples**whatever of B and D ( constr . ) , and G , H any whatever of A and ̊C ; therefore 4. As B is to A , so is ... Página 174

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**equimultiples**whatever D and E , and of C any multiple whatever F. Demonstration . Because D is the same multiple of ...**equimultiples**of A , B ( constr . ) , and F is any mul- tiple of C ; therefore 2. As A is to C , so is B to C ( V ...### 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.