The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, The Book of Euclid's Data, in Like Manner Corrected. viz. the first six books, together with the eleventh and twelfthMathew Carey, and sold by J. Conrad & Company, S. F. Bradford, Birch & Small, and Samuel Etheridge. Printed by T. & G. Palmer, 116, High-Street., 1806 - 518 σελίδες |
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Σελίδα 120
... proportion , is the similitude of ratios . " IX . Proportion consists in three terms at least . X. When three magnitudes are proportionals , the first is said to have to the third the duplicate ratio of that which it has to the second ...
... proportion , is the similitude of ratios . " IX . Proportion consists in three terms at least . X. When three magnitudes are proportionals , the first is said to have to the third the duplicate ratio of that which it has to the second ...
Σελίδα 121
... the fourth . 17th prop . book 5 . XVII . Convertendo , by conversion ; when there are four proportion- als , and it is inferred , that the first is to its excess above the Q Book V. second , as the third to its excess OF EUCLID . 121.
... the fourth . 17th prop . book 5 . XVII . Convertendo , by conversion ; when there are four proportion- als , and it is inferred , that the first is to its excess above the Q Book V. second , as the third to its excess OF EUCLID . 121.
Σελίδα 122
... proportion . It is demonstrated in 22d prop . book 5 . XX . Ex æquali , in proportione perturbata , seu inordinata ; from equa- lity , in perturbate or disorderly proportion * ; this term is used when the first magnitude is to the ...
... proportion . It is demonstrated in 22d prop . book 5 . XX . Ex æquali , in proportione perturbata , seu inordinata ; from equa- lity , in perturbate or disorderly proportion * ; this term is used when the first magnitude is to the ...
Σελίδα 162
... proportion- als . Wherefore , as AB to c 4.6 . d 11. 5 . e 9. 5 . f 8. 1 . g 4.1 . A B 4 E G BC , so is GE to EF ; but as AB to BC , so is DE to EF ; there- fore as DE to EF , sod GE to EF : therefore DE and GE have the same ratio to EF ...
... proportion- als . Wherefore , as AB to c 4.6 . d 11. 5 . e 9. 5 . f 8. 1 . g 4.1 . A B 4 E G BC , so is GE to EF ; but as AB to BC , so is DE to EF ; there- fore as DE to EF , sod GE to EF : therefore DE and GE have the same ratio to EF ...
Σελίδα 170
... proportion- al : and parallelograms that have one angle of the one equal to one angle of the other , and their sides about the equal angles reciprocally proportional , are equal to one another . F Let AB , BC be equal parallelograms ...
... proportion- al : and parallelograms that have one angle of the one equal to one angle of the other , and their sides about the equal angles reciprocally proportional , are equal to one another . F Let AB , BC be equal parallelograms ...
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altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given point given ratio given straight line gnomon greater join less Let ABC meet multiple opposite parallel parallelogram perpendicular point F polygon prisms proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure right angles segment sides BA similar sine solid angle solid parallelepipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Δημοφιλή αποσπάσματα
Σελίδα 30 - Any two sides of a triangle are together greater than the third side.
Σελίδα 64 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Σελίδα 30 - 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. Let...
Σελίδα 59 - PROP. VIII. THEOR. IF a straight line be divided into any two parts, tour times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Σελίδα 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Σελίδα 165 - 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 19 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Σελίδα 191 - In right angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal to the similar, and similarly described figures upon the sides containing the right angle.
Σελίδα 39 - 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 sidef. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.
Σελίδα 180 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.