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 Cushing & Jewett, J. Robinson printer, 1822 - 326 σελίδες |
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Σελίδα 36
... theo . ) GEB⇒CFH , and AEG = EFD . 2. Also GEB - AEF , and CFI EFD , but GEB = CFI ( by part 1. of this theo . ) therefore AEF = EFD . The same way we prove FEC = EFB . 3 . AEF EFD ; ( by the last part of this theo . ) but AEF = GEB ( by ...
... theo . ) GEB⇒CFH , and AEG = EFD . 2. Also GEB - AEF , and CFI EFD , but GEB = CFI ( by part 1. of this theo . ) therefore AEF = EFD . The same way we prove FEC = EFB . 3 . AEF EFD ; ( by the last part of this theo . ) but AEF = GEB ( by ...
Σελίδα 37
... theo . ) and again , since AC cuts the same parallels , the angle ACE = A ( by part 2. of the last . ) Therefore ECD + ACE = B + A . Q. E. D. THEOREM V. In any triangle ABC , all the three angles taken together are equal to two right ...
... theo . ) and again , since AC cuts the same parallels , the angle ACE = A ( by part 2. of the last . ) Therefore ECD + ACE = B + A . Q. E. D. THEOREM V. In any triangle ABC , all the three angles taken together are equal to two right ...
Σελίδα 39
... theo . 4. ) but since AC = CD being radii of the same sircle , it is plain ( by the preceding lemma , ) that the angles subtended by them will also be equal , and that their sum is double to either of them , that THEOREMS . 39.
... theo . 4. ) but since AC = CD being radii of the same sircle , it is plain ( by the preceding lemma , ) that the angles subtended by them will also be equal , and that their sum is double to either of them , that THEOREMS . 39.
Σελίδα 41
... 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 42
... theo . 6. ) AF = FB ; but in the same circle , equal linesa re chords of equal arcs , since they measure them ( by def . 19. ) whence the arc AF - FB , and so AFB is bi- sected in F , by the line CF. Cor . Hence the sine of an arc is ...
... theo . 6. ) AF = FB ; but in the same circle , equal linesa re chords of equal arcs , since they measure them ( by def . 19. ) whence the arc AF - FB , and so AFB is bi- sected in F , by the line CF. Cor . Hence the sine of an arc is ...
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A Treatise of Practical Surveying: Which is Demonstrated From Its First ... Robert Gibson Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2021 |
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20 perches ABCD acres altitude Answer base bearing blank line centre chains and links chord circle circumferentor Co-secant co-sine Co-tang column compass contained cyphers decimal decimal fraction difference Dist divided divisor draw east edge EXAMPLE feet field-book figures four-pole chains given angle half the sum height Hence hypothenuse inches instrument latitude length logarithm measure meridian distance multiplied needle number of degrees object off-sets opposite parallel parallelogram perpendicular piece of ground plane polygon Portmarnock PROB proportion protractor quotient radius right angles right line scale of equal SCHOLIUM secant second station sect semicircle side sights sine square root stationary distance stationary line sun's suppose survey taken tang tangent thence theo theodolite THEOREM thro triangle ABC trigonometry true amplitude true azimuth two-pole chains vane variation whence