A Treatise on Practical Surveying: Which is Demonstrated from Its First Principles, Wherein Every Thing that is Useful and Curious in that Art, is Fully Considered and ExplainedF. Lucas, Jun. and Joseph Cushing, 1816 - 472 σελίδες |
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Σελίδα 40
... theo . ) GEB = CFH , and AEG = HFD . 2. Also GEB = AEF , and CFH - EFD ; but GEB = CFH ( by part 1. of this theo . ) therefore AEF = EFD . The same way we prove FEC = EFB . ( 78 = 7 3. AEF - EFD by the last part of this theo . ) but AEF ...
... theo . ) GEB = CFH , and AEG = HFD . 2. Also GEB = AEF , and CFH - EFD ; but GEB = CFH ( by part 1. of this theo . ) therefore AEF = EFD . The same way we prove FEC = EFB . ( 78 = 7 3. AEF - EFD by the last part of this theo . ) but AEF ...
Σελίδα 41
... theo . ) and again , since AC cuts the same parallels , the angle ACE - A ( by part 2. of the last . ) Therefore ECD + ACE = ACD = B + A . Q. E. D. THEOREM V. In any triangle ABC , all the three angles taken to- gether are equal to two ...
... theo . ) and again , since AC cuts the same parallels , the angle ACE - A ( by part 2. of the last . ) Therefore ECD + ACE = ACD = B + A . Q. E. D. THEOREM V. In any triangle ABC , all the three angles taken to- gether are equal to two ...
Σελίδα 43
... theo . 4. ) but since ACCD being radii of the same circle , it is plain ( by the preceding lemma ) that the an- gles subtended by them will be also equal , and that their sum is double to either of them , that THEOREMS . 43.
... theo . 4. ) but since ACCD being radii of the same circle , it is plain ( by the preceding lemma ) that the an- gles subtended by them will be also equal , and that their sum is double to either of them , that THEOREMS . 43.
Σελίδα 45
... theo . 5. ) then have we AC , CD , and the angle ACD in one triangle ; severally equal to CB , CD , and the angle BCD in the other : therefore ( by theo . 6. ) A = DB . Q. E. D. Cor . Hence it follows , that any line bisecting a chord ...
... theo . 5. ) then have we AC , CD , and the angle ACD in one triangle ; severally equal to CB , CD , and the angle BCD in the other : therefore ( by theo . 6. ) A = DB . Q. E. D. Cor . Hence it follows , that any line bisecting a chord ...
Σελίδα 46
... theo . 6. ) AF = FB ; but in the same circle , equal lines are chords of equal arcs , since they measure them ( by def . 19. ) whence the arc AF = FB , and so AFB is bisected in F , by the line CF. Cor . Hence the sine of an arc is half ...
... theo . 6. ) AF = FB ; but in the same circle , equal lines are chords of equal arcs , since they measure them ( by def . 19. ) whence the arc AF = FB , and so AFB is bisected in F , by the line CF. Cor . Hence the sine of an arc is half ...
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