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 |
Fra bogen
Resultater 1-5 af 100
Side 3
... line given in position . Let A and B be the given points , and CD the given straight line . Join AB , and bisect it in F , and from F draw FE at right angles to AB meet- ing CD in E , E is the point required . Join AE , EB . Since AF FB ...
... line given in position . Let A and B be the given points , and CD the given straight line . Join AB , and bisect it in F , and from F draw FE at right angles to AB meet- ing CD in E , E is the point required . Join AE , EB . Since AF FB ...
Side 5
... lines equal to each other , viz . one on each side of AD . Make DE = DF and join AE . Then ... line more remote is equal to one nearer the perpendi- cular , which is ... required . Draw AE parallel to BD , and .. perpendicular to EF . The ...
... lines equal to each other , viz . one on each side of AD . Make DE = DF and join AE . Then ... line more remote is equal to one nearer the perpendi- cular , which is ... required . Draw AE parallel to BD , and .. perpendicular to EF . The ...
Side 6
... required to draw a line through P which shall be terminated by the given lines , and divided in any given ratio in P , draw PD parallel to AC and take AD : DE in the given ratio and draw EPF , it will be the line required . ( 10. ) From ...
... required to draw a line through P which shall be terminated by the given lines , and divided in any given ratio in P , draw PD parallel to AC and take AD : DE in the given ratio and draw EPF , it will be the line required . ( 10. ) From ...
Side 7
... line required . A D P E For since DE is parallel to AC , ( Eucl . vi . 2. ) DB : BE :: AB : BC , i . e . in the given ratio . ( 12. ) If from a given point any number of straight lines be drawn to a straight line given in position , to ...
... line required . A D P E For since DE is parallel to AC , ( Eucl . vi . 2. ) DB : BE :: AB : BC , i . e . in the given ratio . ( 12. ) If from a given point any number of straight lines be drawn to a straight line given in position , to ...
Side 8
... line . Let ABC be the given angle , DE parallel to AB , and P the given point . From P draw PC parallel B с A D to DE or AB , and take BE : CF in the given ratio . Join FP and produce it to A ; APF is the line required . For since DE ...
... line . Let ABC be the given angle , DE parallel to AB , and P the given point . From P draw PC parallel B с A D to DE or AB , and take BE : CF in the given ratio . Join FP and produce it to A ; APF is the line required . For since DE ...
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 | |
75 | |
80 | |
86 | |
87 | |
91 | |
92 | |
97 | |
103 | |
109 | |
114 | |
120 | |
126 | |
134 | |
171 | |
177 | |
179 | |
185 | |
191 | |
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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