A Treatise of Practical Surveying: Which is Demonstrated from Its First Principles. Wherein Every Thing that is Useful and Curious in that Art, is Fully Considered and Explained ... The Whole Illustrated with CopperplatesP. Wogan, 1795 - 319 σελίδες |
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Σελίδα 18
... plain , Fig . 8 . 1. That any Chord will divide the Circle into two Segments . 2. The lefs the Chord is , the more unequal are the Segments . 3. When the Chord is greatest it becomes a Diameter , and then the Segments are equal ; and ...
... plain , Fig . 8 . 1. That any Chord will divide the Circle into two Segments . 2. The lefs the Chord is , the more unequal are the Segments . 3. When the Chord is greatest it becomes a Diameter , and then the Segments are equal ; and ...
Σελίδα 33
... twice that Arc . For AD is the Sine of the Arc AF , ( by Def . 22. ) AF is half the Arc , and AD half the Chord AB ( by Theo . 8. ) Th.re- .fore the Cor . is plain . F 7 H E 0 . Plate I. In THEO . X. any Triangle ABD , THEOREM S. 33.
... twice that Arc . For AD is the Sine of the Arc AF , ( by Def . 22. ) AF is half the Arc , and AD half the Chord AB ( by Theo . 8. ) Th.re- .fore the Cor . is plain . F 7 H E 0 . Plate I. In THEO . X. any Triangle ABD , THEOREM S. 33.
Σελίδα 35
... plain , that the oppo- fite Sides of a Parallelogram are equal ; for it has been proved that ABCD being a Parallelogram , AB will be CD and AD = BC . THE O. XIII . All Parallelograms on the fame or equal Bafes and between the fame ...
... plain , that the oppo- fite Sides of a Parallelogram are equal ; for it has been proved that ABCD being a Parallelogram , AB will be CD and AD = BC . THE O. XIII . All Parallelograms on the fame or equal Bafes and between the fame ...
Σελίδα 36
... plain that Triangles on the fame or equal Bafes , and between the fame Paral- lels , are equal , feeing ( by Cor . 2. Theo . 12. ) they are the Halves of their refpective Parallelograms . P THE O. XIV . In every right - angled Triangle ...
... plain that Triangles on the fame or equal Bafes , and between the fame Paral- lels , are equal , feeing ( by Cor . 2. Theo . 12. ) they are the Halves of their refpective Parallelograms . P THE O. XIV . In every right - angled Triangle ...
Σελίδα 38
... plain fince the Angle A = a , the Arc BDC = bdc , and confequently the Chord BC is to bc , as the Radius of the Circle ABC is to the Radius of the Circle abc ; ( for the greater the Radius is , the greater is the Circle defcribed by ...
... plain fince the Angle A = a , the Arc BDC = bdc , and confequently the Chord BC is to bc , as the Radius of the Circle ABC is to the Radius of the Circle abc ; ( for the greater the Radius is , the greater is the Circle defcribed by ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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Δημοφιλή αποσπάσματα
Σελίδα 13 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees; and each degree into 60 minutes, each minute into 60 seconds, and so on.
Σελίδα 88 - 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 56 - ... logarithm of that number. EXAMPLE. • Required, the logarithm of 365. Answer, 2.56229. And though most tables of logarithms run but to 10000, yet by them the log. of any number not exceeding 10,000,000 may be found, and on the contrary, the number to any such logarithm, thus : 1 Find the log. of the first four figures of the given number 2. Take that log. from the log: of the number next following, and note their difference, 3. Multiply that difference by the remaining figures of the given number...
Σελίδα 91 - In the triangle ABC, there is given AB 240, the angle A 46° 30', and BC 200, to find the angle C, being acute, the angle B, and the side AC.
Σελίδα 89 - ED. that is as the sum of the two sides AB and BC, is to their difference ; so is the tangent of half the sum of the two unknown angles A and C, to the tangent of half their difference.
Σελίδα 32 - 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 19 - 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. POSTULATES OR PETITIONS. 1 . That a right line may be drawn from any one given point to another. 2. That a right line may be produced or continued at pleasure. 3. That from any centre and with any radius, the circumference of a circle may be described.
Σελίδα 13 - A chord is a right line drawn from one end of an arc or arch (that is, any part of the circumference of a circle) to the other ; and is the measure of the arc. Thus the right line HG, is the measure of the arc HBG.
Σελίδα 72 - ... these three proportions, for DE we put its equal be, for AE put ab, and for AD put ac, they will become AB : ab : : AC : ас, and AB : ab : : BC : be, and AC : ac : : BC : be.
Σελίδα 285 - Then if the true and magnetic amplitudes, be both north or both south, their difference is the variation ; but if one be north and the other south, their sum is the variation ; and to know whether it be easterly or westerly, suppose the observer looking...