The Elements of EuclidDesilver, Thomas, 1838 - 416 páginas |
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Página 250
... given in that book , as in this : but indeed there is scarce any need of it ... species of compound ratio . But Theon has made it the 5th def . of book 6 ... given , but they retain also Theon's , which they ought to have left out of the ...
... given in that book , as in this : but indeed there is scarce any need of it ... species of compound ratio . But Theon has made it the 5th def . of book 6 ... given , but they retain also Theon's , which they ought to have left out of the ...
Página 293
... given in magnitude , when equals to them can be found . II . A ratio is said to be given , when a ratio of a given ... species , which have each of their angles given , and the ratios of their sides given . IV . Points , lines , and ...
... given in magnitude , when equals to them can be found . II . A ratio is said to be given , when a ratio of a given ... species , which have each of their angles given , and the ratios of their sides given . IV . Points , lines , and ...
Página 316
... given ; and therefore ( cor . 6 . or 7. dat . ) the ratio of ML to LN is given ; but LM is given in mag- nitude ... species . Ꭰ Let each of the sides of the triangle ABC be given in magnitude , the triangle ABC is given in species ...
... given ; and therefore ( cor . 6 . or 7. dat . ) the ratio of ML to LN is given ; but LM is given in mag- nitude ... species . Ꭰ Let each of the sides of the triangle ABC be given in magnitude , the triangle ABC is given in species ...
Página 317
... given in magnitude , the triangle is given in species . Let each of the angles of the triangle ABC be given in magnitude , the triangle ABC is given in species . B A D CE F Take a straight line DE given in po- sition and magnitude , and ...
... given in magnitude , the triangle is given in species . Let each of the angles of the triangle ABC be given in magnitude , the triangle ABC is given in species . B A D CE F Take a straight line DE given in po- sition and magnitude , and ...
Página 318
... given in species , and therefore also the triangle ABC . PROP . XLV . 42 . Ir the sides of a triangle have to one another given ratios , the triangle is given in species . Let the sides of the triangle ABC have given ratios to one ...
... given in species , and therefore also the triangle ABC . PROP . XLV . 42 . Ir the sides of a triangle have to one another given ratios , the triangle is given in species . Let the sides of the triangle ABC have given ratios to one ...
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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 square of BC straight line AB straight line BC tangent THEOR triangle ABC triplicate ratio vertex wherefore
Pasajes populares
Página 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.
Página 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.
Página 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.
Página 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.
Página 9 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Página 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.
Página 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.
Página 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.
Página 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...
Página 131 - ... rectilineal figures are to one another in the duplicate ratio of their homologous sides.