The Elements of EuclidDesilver, Thomas, 1838 - 416 sider |
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Side 93
... 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 ... proportionals , it THE ...
... 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 ... proportionals , it THE ...
Side 94
... proportionals , the first is said to have to the third the duplicate ratio of that which it has to the second . XI . When four magnitudes are continual proportionals , the first is said to have to the fourth the triplicate ratio of that ...
... proportionals , the first is said to have to the third the duplicate ratio of that which it has to the second . XI . When four magnitudes are continual proportionals , the first is said to have to the fourth the triplicate ratio of that ...
Side 95
... proportionals . ' XIII . Permutando , or alternando , by permutation , or alternately ; this word is used when there are four proportionals , and it is inferred , that the first has the same ratio to the third , which the second has to ...
... proportionals . ' XIII . Permutando , or alternando , by permutation , or alternately ; this word is used when there are four proportionals , and it is inferred , that the first has the same ratio to the third , which the second has to ...
Side 101
... it , the third can be proved to be equal to the fourth , or less than it . Therefore , if the first , & c . Q. E. D. * See Notes .. PROP . B. THEOR . IF four magnitudes be proportionals BOOK V. 101 THE ELEMENTS OF EUCLID .
... it , the third can be proved to be equal to the fourth , or less than it . Therefore , if the first , & c . Q. E. D. * See Notes .. PROP . B. THEOR . IF four magnitudes be proportionals BOOK V. 101 THE ELEMENTS OF EUCLID .
Side 102
Euclid Robert Simson. PROP . B. THEOR . IF four magnitudes be proportionals they are poportionals also when taken inversely . " If the magnitude A be to B , as C is to D , then also inversely B is to A , as D , to C. Take of B and D any ...
Euclid Robert Simson. PROP . B. THEOR . IF four magnitudes be proportionals they are poportionals also when taken inversely . " If the magnitude A be to B , as C is to D , then also inversely B is to A , as D , to C. Take of B and D any ...
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altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gles gnomon greater join less Let ABC multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopiped square of AC square of BC straight line AB straight line BC tangent THEOR triangle ABC triplicate ratio vertex wherefore
Populære avsnitt
Side 34 - 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 at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Side 143 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical 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 the base, together with the square on the straight line which bisects the angle.
Side 63 - 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.
Side 246 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Side 9 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Side 119 - 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.
Side 19 - 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.
Side 12 - To construct a triangle of which the sides shall be equal to three given straight lines ; but any two whatever of these lines must be greater than the third (20.
Side 78 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Side 131 - ... rectilineal figures are to one another in the duplicate ratio of their homologous sides.