## The Elements of Euclid, the parts read in the University of Cambridge [book 1-6 and parts of book 11,12] with geometrical problems, by J.W. Colenso1846 |

### Dentro del libro

Resultados 1-5 de 52

Página 153

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**Ratio**is a mutual relation of two magnitudes of the same kind to one another in respect of quantity . IV . Magnitudes are said to have a**ratio**to one another , when the less can be multiplied so as to exceed the other . v . The first of ... Página 154

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**ratio**than the third has to the fourth , and the third is said to have to the fourth a less**ratio**than the first has to the second . VIII . Analogy , or proportion , is the similitude of**ratios**. IX . Proportion consists in three terms ... Página 155

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**ratio**which A has to D ; then , for shortness ' sake , M is said to have to N the**ratio**compounded of the**ratios**of E to F , G to H , and K to L. XII . In proportionals , the antecedent terms are said to be homologous to one another ... Página 160

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**ratio**to the second which the t'ird has to the fourth , and if of the first and third there be taken any equimultiples whatever , and also any whatever of the second and fourth , then the multiple of the first shall have the same**ratio**... Página 161

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**ratio**to the second and fourth , and , in like manner , the first and the third shall have the same**ratio**to any equimultiples whatever of the second and fourth . Let A the first have to B the second , the same**ratio**which C , the third ...### Otras ediciones - Ver todas

The Elements of Euclid, the Parts Read in the University of Cambridge [Book ... Euclides Sin vista previa disponible - 2016 |

### Términos y frases comunes

ABCD adjacent angles angle ABC angle ACB angle BAC angle BCD angle EDF angle equal base BC BC is equal centre chord circle ABC circumference cuts the circle diameter double draw equal angles equal to F equiangular equilateral triangle equimultiples exterior angle fore given circle given line given point given straight line gnomon greater ratio inscribed intersection isosceles triangle less Let ABC Let the straight lines be drawn lines drawn meet multiple opposite angles opposite sides parallel to BC parallelogram pentagon perpendicular plane polygon PROB produced proportionals Q.E.D. PROP rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn square of AC straight line &c straight line AB THEOR touches the circle triangle ABC twice the rectangle Wherefore

### Pasajes populares

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 4 - Let it be granted that a straight line may be drawn from any one point to any other point.

Página 33 - F, which is the common vertex of the triangles: that is », together with four right angles. 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.

Página 62 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.

Página 22 - If from the ends of a side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle.

Página 58 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.

Página 146 - ... may be demonstrated from what has been said of the pentagon : and likewise a circle may be inscribed in a given equilateral and equiangular hexagon, and circumscribed about it, by a method like to that used for the pentagon.

Página 194 - 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 2 - 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 : 16.

Página 69 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.