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 1
... ( Eucl . i . 32. ) and consequently less than ACD . But the greater angle is subtended by the greater side ( Eucl . i . 19. ) ; therefore AD is greater than AC . In the same manner every other line drawn from A to BD may be shewn to be ...
... ( Eucl . i . 32. ) and consequently less than ACD . But the greater angle is subtended by the greater side ( Eucl . i . 19. ) ; therefore AD is greater than AC . In the same manner every other line drawn from A to BD may be shewn to be ...
Side 2
... ( Eucl . i . 20. ) ; therefore , & c . ( 3. ) Through a given point to draw a straight line which shall make equal angles with two straight lines given in position . Let P be the given point , and BE , CF the lines given in position ...
... ( Eucl . i . 20. ) ; therefore , & c . ( 3. ) Through a given point to draw a straight line which shall make equal angles with two straight lines given in position . Let P be the given point , and BE , CF the lines given in position ...
Side 5
... ( Eucl . i . 16. ) , and therefore greater than AGF , hence ( Eucl . i . 19. ) AG is greater than AF . In the same manner it may be shewn that AH is greater than AG . · = And from A there can only be drawn to BC two straight lines equal ...
... ( Eucl . i . 16. ) , and therefore greater than AGF , hence ( Eucl . i . 19. ) AG is greater than AF . In the same manner it may be shewn that AH is greater than AG . · = And from A there can only be drawn to BC two straight lines equal ...
Side 6
... ( Eucl . vi . 2. ) EP : PF :: ED : DA , i . e . in a ratio of equality . COR . If it be 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 ...
... ( Eucl . vi . 2. ) EP : PF :: ED : DA , i . e . in a ratio of equality . COR . If it be 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 ...
Side 7
... ( 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 determine the locus of the points of section which divide ...
... ( 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 determine the locus of the points of section which divide ...
Indhold
1 | |
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 | |
193 | |
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