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, 1837 - 318 σελίδες |
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Αποτελέσματα 6 - 10 από τα 17.
Σελίδα 113
... Equal magnitudes have the same ratio to the same magnitude ; and the same has the same ratio to equal magnitudes . Let A and B be equal magnitudes , and C any other ; A : C :: B : C. Let mA , mB , be any equimultiples of A and B ; and ...
... Equal magnitudes have the same ratio to the same magnitude ; and the same has the same ratio to equal magnitudes . Let A and B be equal magnitudes , and C any other ; A : C :: B : C. Let mA , mB , be any equimultiples of A and B ; and ...
Σελίδα 114
... equal to the same ratio are equal to one another . If A : B :: C : D ; and also C : D :: E : F ; then A : B :: E : F. Take mA , mC , mE , any equimultiples of A , C , and E ; and nB , nD , nF , any equimultiples of B , D , and F ...
... equal to the same ratio are equal to one another . If A : B :: C : D ; and also C : D :: E : F ; then A : B :: E : F. Take mA , mC , mE , any equimultiples of A , C , and E ; and nB , nD , nF , any equimultiples of B , D , and F ...
Σελίδα 115
... equimultiples of A , C , and E ; and nB , nD , nF , any equimultiples of B , D , and F. Then , because A : B :: C : D , if mA 7mB , nC7nD ( def . 5. 5. ) ; and when mC7nD , mE 7nF , because C : D E F. Therefore , if mA 7nB , mA + mC + ...
... equimultiples of A , C , and E ; and nB , nD , nF , any equimultiples of B , D , and F. Then , because A : B :: C : D , if mA 7mB , nC7nD ( def . 5. 5. ) ; and when mC7nD , mE 7nF , because C : D E F. Therefore , if mA 7nB , mA + mC + ...
Σελίδα 116
... equimultiples of A and B. : PROP . XVI . THEOR . If four magnitudes of the same kind be proportionals , they will also be pro- portionals when taken alternately . If A : B :: C : D , then alternately , A : C1 .: B : D. Take mA , mB any ...
... equimultiples of A and B. : PROP . XVI . THEOR . If four magnitudes of the same kind be proportionals , they will also be pro- portionals when taken alternately . If A : B :: C : D , then alternately , A : C1 .: B : D. Take mA , mB any ...
Σελίδα 118
... equimultiples whatever , mA , mD ; and of B and D any whatever , nB , nand of C and F any whatever , qC , qF ... equimultiples of A and D ; and qC , qF are any equimultiples of C and F ; therefore :: D : F. Again , let there be ...
... equimultiples whatever , mA , mD ; and of B and D any whatever , nB , nand of C and F any whatever , qC , qF ... equimultiples of A and D ; and qC , qF are any equimultiples of C and F ; therefore :: D : F. Again , let there be ...
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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 Let the straight 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 spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore
Δημοφιλή αποσπάσματα
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 12 - AB; but things which are equal to the same are equal to one another...
Σελίδα 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.
Σελίδα 288 - 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 35 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Σελίδα 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 this line with the line which touches the circle, shall be equal to the angles in the alternate segments of the circle.
Σελίδα 52 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.
Σελίδα 127 - 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.
Σελίδα 23 - If, from the ends of the 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.
Σελίδα 19 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it the angles CBA, ABD ; these are either two right angles, or are together equal to two right angles. For, if the angle CBA be equal to ABD, each of them is a right angle (Def.