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 GeometryW. E. Dean, 1845 - 317 σελίδες |
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Αποτελέσματα 1 - 5 από τα 59.
Σελίδα 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 : A B thus , 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 : A B thus , signifies the ratio or quotient arising from the division of the quantity A by B. In fact ...
Σελίδα 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 • ...
... 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 • ...
Σελίδα 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 ...
Σελίδα 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 I .. 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 I .. 11. If ...
Σελίδα 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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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 third touches the circle triangle ABC triangle DEF wherefore
Δημοφιλή αποσπάσματα
Σελίδα 50 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Σελίδα 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.
Σελίδα 16 - If two triangles have two sides of the one equal to two sides of the other...
Σελίδα 28 - If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite angle upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.
Σελίδα 13 - From the greater of two given straight lines to cut off a part equal to the less.
Σελίδα 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.
Σελίδα 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.
Σελίδα 149 - ... cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Σελίδα 30 - 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.
Σελίδα 21 - Any two angles of a triangle are together less than two right angles, Let ABC be any triangle ; any two of its angles together are less than two right angles.