A Treatise of Practical Surveying, ...1808 - 440 σελίδες |
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Σελίδα 26
... the angles made by these lines will be equal to two right angles . 2. And all the angles which can be made about a point , will be equal to four right angles . Plate I. THEO . II . If one right line THEO . GEOMETRIAL ...
... the angles made by these lines will be equal to two right angles . 2. And all the angles which can be made about a point , will be equal to four right angles . Plate I. THEO . II . If one right line THEO . GEOMETRIAL ...
Σελίδα 27
... THEO . III . If a right line cross two parallels , as GH does AB and CD . ( fig . 22. ) then , 1. Their external angles are equal to each other , that is , GEB CFH . 2. The alternate angles will be equal , that is , AEF EFD and BEF ...
... THEO . III . If a right line cross two parallels , as GH does AB and CD . ( fig . 22. ) then , 1. Their external angles are equal to each other , that is , GEB CFH . 2. The alternate angles will be equal , that is , AEF EFD and BEF ...
Σελίδα 28
... theo . ) GEB⇒CFH , and AEG HFD . 2. Also GEBAEF , and CFH - EFD ; but GEB = CFH ( by part 1. of this theo . ) therefore AEF EFD . The same way we prove FEB ÷ EFC . 3. AEFEFD ; ( by the last part of this theo . ) but AEF GEB ( by theo ...
... theo . ) GEB⇒CFH , and AEG HFD . 2. Also GEBAEF , and CFH - EFD ; but GEB = CFH ( by part 1. of this theo . ) therefore AEF EFD . The same way we prove FEB ÷ EFC . 3. AEFEFD ; ( by the last part of this theo . ) but AEF GEB ( by theo ...
Σελίδα 29
... theo . ) and again , since AC cuts the same parallels , the angle ACEA ( by part 2. of the last . ) Therefore ECD + ACE = ACD = B + A . Q. E. D. THEO . 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 ACEA ( by part 2. of the last . ) Therefore ECD + ACE = ACD = B + A . Q. E. D. THEO . V. In any triangle ABC , all the three angles taken together are equal to two right ...
Σελίδα 31
... theo . 4. ) but since ACCD being radii of the same circle , it is plain ( by the pre- ceding lemma ) that the angles subtended by them will be also equal , and that their sum is double to either of them , that is , DAC + ADC is double ...
... theo . 4. ) but since ACCD being radii of the same circle , it is plain ( by the pre- ceding lemma ) that the angles subtended by them will be also equal , and that their sum is double to either of them , that is , DAC + ADC is double ...
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A Treatise of Practical Surveying: Which Is Demonstrated From Its First ... Robert Gibson Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
A Treatise of Practical Surveying: Which Is Demonstrated from Its First ... Department of Radiology Royal Melbourne Hospital Robert Gibson,Robert Gibson Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
A Treatise of Practical Surveying: Which Is Demonstrated from Its First ... Department of Radiology Royal Melbourne Hospital Robert Gibson,Robert Gibson Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2013 |
Συχνά εμφανιζόμενοι όροι και φράσεις
40 perches ABCD acres altitude Answer base bearing blank line centre chains and links chord circle circumferentor Co-fecant Secant Co-fine Co-tang column contained cyphers decimal decimal fraction diameter difference Dift Diſt distance line divided draw drawn east edge EXAMPLE feet field-book figures fore four-pole chains half the sum height hypothenuse inches instrument latitude logarithm measure meridian distance method multiplied needle number of degrees object off-sets parallel parallelogram perpendicular piece of ground plane Plate pole Portmarnock PROB protractor quotient radius right angles right line scale of equal second station sect semicircle side sights sine square root stationary distance stationary line sun's survey taken tangent thence theo theodolite thro trapezium triangle ABC trigonometry true amplitude two-pole chains vane variation Vulgar Fraction whence ΙΟ
Δημοφιλή αποσπάσματα
Σελίδα 32 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Σελίδα 199 - ... that triangles on the same base and between the same parallels are equal...
Σελίδα 94 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Σελίδα 23 - Four quantities are said to be in proportion when the product of the extremes is equal to that of the means : thus if A multiplied by D, be equal to B multiplied by C, then A is said to be to B as C is to D.
Σελίδα 95 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Σελίδα 37 - ABDE+ACGF the sum of the squares —BKLH-\-KCML, the sum of the two parallelograms or square BCMH; therefore the sum of the squares on AB and AC is equal to the square on BC.
Σελίδα 24 - Things that are equal to one and the same thing, are equal to each other. 2. Every whole is greater than its part. % 3. Every whole is equal to all its parts taken together. 4 If to equal things, equal things be added, the whole will be equal. 5. If from equal things, equal things be deducted the remainders will be equal.
Σελίδα 36 - XIII. •All parallelograms on the same or equal bases and between the same parallels...
Σελίδα 182 - VI. To find the content of a triangular piece of ground, Multiply the base by half the perpendicular, or the perpendicular by half the base ; or take half the product of the base into the perpendicular. The reason hereof is plain, from cor.
Σελίδα 35 - Triangles upon equal bases, and between the same parallels, are equal to one another.