Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids : to which are Added, Elements of Plane and Spherical TrigonometryW. E. Dean, 1842 - 317 páginas |
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Página 7
... ratio of one quantity to another , is usually denoted by placing one of the two quantities over the other , in the form of a fraction : thus , A B signifies the ratio or quotient arising from the division of the quantity A by B. In fact ...
... ratio of one quantity to another , is usually denoted by placing one of the two quantities over the other , in the form of a fraction : thus , A B signifies the ratio or quotient arising from the division of the quantity A by B. In fact ...
Página 106
... greater contains the less a cer- tain number of times exactly . 3. Ratio is a mutual relation of two magnitudes , of the same kind , to one another , in respect of quantity . 4. Magnitudes are said to be of the same kind ELEMENTS ...
... greater contains the less a cer- tain number of times exactly . 3. Ratio is a mutual relation of two magnitudes , of the same kind , to one another , in respect of quantity . 4. Magnitudes are said to be of the same kind ELEMENTS ...
Página 107
... ratio to one another . 5. If there be four magnitudes , and if any equimultiples whatsoever be taken of the first ... ratio that the third has to the fourth . 6. Magnitudes are said to be proportionals , when the first has the same ratio ...
... ratio to one another . 5. If there be four magnitudes , and if any equimultiples whatsoever be taken of the first ... ratio that the third has to the fourth . 6. Magnitudes are said to be proportionals , when the first has the same ratio ...
Página 108
... ratio which A has to D , then , for shortness ' sake , M is said to have to Na ratio compounded of the same ratios which compound the ratio of A to D ; that is , a ratio compounded of the ratios of E to F , G to H , and K to L. 11. If ...
... ratio which A has to D , then , for shortness ' sake , M is said to have to Na ratio compounded of the same ratios which compound the ratio of A to D ; that is , a ratio compounded of the ratios of E to F , G to H , and K to L. 11. If ...
Página 111
... ratio to the second which the third has to the fourth , and if any equimultiples whatever be taken of the first and third , and any whatever of the second and fourth ; the multiple of the first shall have the same ratio to the multiple ...
... ratio to the second which the third has to the fourth , and if any equimultiples whatever be taken of the first and third , and any whatever of the second and fourth ; the multiple of the first shall have the same ratio to the multiple ...
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Términos y frases comunes
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore
Pasajes populares
Página 51 - 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 149 - IF an angle of a triangle be bisected by a straight line, which likewise cuts the base ; the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of...
Página 12 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line.
Página 9 - 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 52 - If a straight line be bisected, and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Página 80 - 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 296 - 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 50 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Página 15 - 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 extremity.
Página 81 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles made by...