The Elements of EuclidDesilver, Thomas, 1838 - 416 páginas |
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Página 93
... third is also greater than that of the fourth . VI . Magnitudes which have the same ratio are called proportionals . ، N. B. When four magnitudes are proportionals , it. * See Note . * See Note . * See Note . * See THE ...
... third is also greater than that of the fourth . VI . Magnitudes which have the same ratio are called proportionals . ، N. B. When four magnitudes are proportionals , it. * See Note . * See Note . * See Note . * See THE ...
Página 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 ...
... 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 ...
Página 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 ...
Página 101
... to the fourth , or less than it . Therefore , if the first , & c . Q. E. D. PROP . B. THEOR . Ir four magnitudes be proportionals. * See Notes . * See Notes . BCD EGFH * See Note . BOOK V. 101 THE ELEMENTS OF EUCLID .
... to the fourth , or less than it . Therefore , if the first , & c . Q. E. D. PROP . B. THEOR . Ir four magnitudes be proportionals. * See Notes . * See Notes . BCD EGFH * See Note . BOOK V. 101 THE ELEMENTS OF EUCLID .
Página 102
Euclid Robert Simson. PROP . B. THEOR . Ir 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 . Ir 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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Términos y frases comunes
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 straight line AB straight line BC tangent THEOR third three plane angles triangle ABC triplicate ratio vertex wherefore
Pasajes populares
Página 36 - 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.
Página 145 - 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.
Página 65 - 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 248 - 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.
Página 11 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Página 121 - 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 21 - 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 14 - 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.
Página 80 - 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...
Página 133 - ... rectilineal figures are to one another in the duplicate ratio of their homologous sides.