Geometrical problems deducible from the first six books of Euclid, arranged and solved. To which is added, an appendix containing the elements of plane trigonometryJ. Smith, Printer to the University; and sold by Nicholson & Son, Deighton & Sons, Thorpe, and Newby, Cambridge; and J. Mawman, and F. C. & J. Rivington, London., 1819 - 377 sider |
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Resultater 1-5 af 19
Side xix
... ratio . 24. If the base of a triangle be produced so that the whole may be to the part produced in the duplicate ratio of the sides ; the line joining the vertex , and the extremity of the part produced will be a mean proportional ...
... ratio . 24. If the base of a triangle be produced so that the whole may be to the part produced in the duplicate ratio of the sides ; the line joining the vertex , and the extremity of the part produced will be a mean proportional ...
Side xli
... duplicate ratio of the adjacent sides . 28. If one circle be circumscribed and another inscribed in a given triangle , and a line be drawn from the vertical angle to the centre of the inner , and produced to the circumference of the ...
... duplicate ratio of the adjacent sides . 28. If one circle be circumscribed and another inscribed in a given triangle , and a line be drawn from the vertical angle to the centre of the inner , and produced to the circumference of the ...
Side 47
... duplicate ratio of AB : AD . For the same reason , AG : AB in the duplicate ratio of AC : AB , .. AG AH in the duplicate ratio of AC : Sect . 2. ] 47 GEOMETRICAL PROBLEMS .
... duplicate ratio of AB : AD . For the same reason , AG : AB in the duplicate ratio of AC : AB , .. AG AH in the duplicate ratio of AC : Sect . 2. ] 47 GEOMETRICAL PROBLEMS .
Side 48
... duplicate ratio of AE : AF , .. ( Eucl . v . 15. ) the duplicate ratio of AC : AD , is the same with the duplicate ratio of AE : AF , and .. AC : AD :: AE : AF . ( 40. ) If three circles , whose diameters are in con- tinued proportion ...
... duplicate ratio of AE : AF , .. ( Eucl . v . 15. ) the duplicate ratio of AC : AD , is the same with the duplicate ratio of AE : AF , and .. AC : AD :: AE : AF . ( 40. ) If three circles , whose diameters are in con- tinued proportion ...
Side 66
Miles Bland. a given ratio , take AB and EF in that ratio , and make the same construction as in the proposition ... duplicate ratio of OC : OD , i . e . in the duplicate ratio of AO : OB . But ( Eucl . vi . 8. Cor . ) AE EB in the ...
Miles Bland. a given ratio , take AB and EF in that ratio , and make the same construction as in the proposition ... duplicate ratio of OC : OD , i . e . in the duplicate ratio of AO : OB . But ( Eucl . vi . 8. Cor . ) AE EB in the ...
Indhold
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6 | |
12 | |
17 | |
19 | |
23 | |
25 | |
30 | |
140 | |
146 | |
147 | |
154 | |
157 | |
158 | |
164 | |
170 | |
36 | |
42 | |
43 | |
47 | |
52 | |
58 | |
63 | |
65 | |
69 | |
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80 | |
86 | |
87 | |
91 | |
92 | |
97 | |
103 | |
109 | |
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126 | |
134 | |
171 | |
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199 | |
203 | |
209 | |
212 | |
218 | |
220 | |
226 | |
232 | |
237 | |
244 | |
249 | |
255 | |
273 | |
295 | |
301 | |
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Almindelige termer og sætninger
ABCD angle ABC angles at F base centre chord circle ABC circles cut circles touch circumference describe a circle divided draw a line Draw the diameter drawn parallel duplicate ratio equal angles equiangular Eucl extremities given angle given circle given in position given line given point given ratio given square given straight line given triangle intercepted isosceles triangle Join AE Join BD Let AB Let ABC let fall line given line joining line required lines be drawn lines drawn mean proportional opposite side parallel to BC parallelogram pendicular perpen point of bisection point of contact point of intersection point required radius rectangle rectangle contained right angles segments semicircle shewn tangent touches the circle trapezium triangle ABC