## The Elements of EuclidDesilver, Thomas, 1838 - 416 páginas |

### Dentro del libro

Resultados 1-5 de 18

Página 94

... 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

... 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 which it has to the second , and so on , quadruplicate , & c ... Página 187

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**triplicate ratio**of their homologous sides . Let AB , CD be similar solid parallelopipeds , and the side AE ho- mologous to the side CF : the solid AB has to the solid CD the tri- plicate ratio of that which AE has to CF. Produce AE ... Página 188

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**triplicate ratio**of that which it has to the second : therefore the solid AB has to the solid KO the**triplicate ratio**of that which AB has to EX : but as AB is to EX , so is the parallelogram AG to the parallelogram GK , and the ... Página 211

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**triplicate ratio**of that of their homologous sides . Let the pyramids having the triangles ABC , DEF for their bases , and the points G , H for their vertices , be similar , and similarly situ- ated ; the pyramid ABCG has to the pyramid ... Página 212

... triplicate ( 33. 11. ) ratio of that which their homologous sides have : therefore the solid BGML has to the solid EHPO the

... triplicate ( 33. 11. ) ratio of that which their homologous sides have : therefore the solid BGML has to the solid EHPO the

**triplicate ratio**of that which the side BC has to the homologous side EF : but as the solid BGML is to the solid ...### Otras ediciones - Ver todas

### 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.