The Doctrine of Plain and Spherical Trigonometry: With Its Application and Use in the Following Parts of Mathematicks : Viz. I. Navigation in All Its Kinds ; as Plain Sailing, Mercator's Sailing, Middle Latitude, and Parallel Sailing, II. Astronomy, Wherein All the Problems Relation to the Doctrine of the Sphere are Solved, III. Projection of the Sphere in Plano, IV. Geography, V. Fortification, VI. Mensuration of Heights and Distances, Both Accessible and Inaccessible, VII. Dialling, Arithmetical and Intrumental, on All Sorts of PlanesJ. Darby, 1725 - 479 σελίδες |
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Σελίδα 56
... Circle , and draw the Lines CE , and BE ; then will the Angle CBE be equal to the Angle CDE ; and also the Angles ECB and EDB are equal ( by Eucl . 3 Lib . 21. Pr . ) Hence all the Angles , and one fide , in the oblique angled Triangle ...
... Circle , and draw the Lines CE , and BE ; then will the Angle CBE be equal to the Angle CDE ; and also the Angles ECB and EDB are equal ( by Eucl . 3 Lib . 21. Pr . ) Hence all the Angles , and one fide , in the oblique angled Triangle ...
Σελίδα 68
... oblique angled Triangles are folved . CHAP . VII . Of the four Fundamental Axioms , for the Solu- tion of Spherical ... Circle CBEG be inclin- ed to another Quadrant CADG , and two other perpendicular Quadrants cut both of them , viz ...
... oblique angled Triangles are folved . CHAP . VII . Of the four Fundamental Axioms , for the Solu- tion of Spherical ... Circle CBEG be inclin- ed to another Quadrant CADG , and two other perpendicular Quadrants cut both of them , viz ...
Σελίδα 168
... oblique angled Spherical Triangles by Projection ; that is , to project any Spherical Triangle to an- fwer any of ... Circle , according to any number of Degrees given ; and alfo to project any greater or leffer Circle of the Sphere ...
... oblique angled Spherical Triangles by Projection ; that is , to project any Spherical Triangle to an- fwer any of ... Circle , according to any number of Degrees given ; and alfo to project any greater or leffer Circle of the Sphere ...
Σελίδα 169
... Circle is required . Rule . From the Chords lay 90 Deg . on the primi- tive Circle from C or D , both ways , to B or E ; fo is B or E the Pole required . CASE 3. The Pole of an oblique Circle is required . Rule . The Pole of the oblique ...
... Circle is required . Rule . From the Chords lay 90 Deg . on the primi- tive Circle from C or D , both ways , to B or E ; fo is B or E the Pole required . CASE 3. The Pole of an oblique Circle is required . Rule . The Pole of the oblique ...
Σελίδα 170
... oblique Circle , and BE at right Angles to that ; draw BG thro F , and from G lay 90 deg . of Chords to H , and draw BH , which will cut AD in a , the Pole of the oblique Circle required . Or the half Tan- gent of the Complement of AF ...
... oblique Circle , and BE at right Angles to that ; draw BG thro F , and from G lay 90 deg . of Chords to H , and draw BH , which will cut AD in a , the Pole of the oblique Circle required . Or the half Tan- gent of the Complement of AF ...
Συχνά εμφανιζόμενοι όροι και φράσεις
acute againſt alfo Altitude Arch Bafe Baſe becauſe Cafe Center Co-fine Comp Compaffes Compl Courfe Courſe Declination defcribe Departure Dial Diff Difference of Latitude Difference of Longitude Diſtance run Eaft Ecliptick equal Equinoctial extent will reach fame fe.c fecond fide find the Angle firft firſt flanking Angle fubtract half Sum half Tangent half the Angle half the Difference half the Sum Hour Hour-Lines Hypothenufe Hypothenufe BC Interfection lay a Ruler leffer lefs Line of Chords Line of Numbers meaſure Meridian muſt North North Plain Obfervation oblique angled oblique Circle obtufe Perpendicular Plain Triangles Points Pole primitive Circle Proportion Quadrant Radius reclining Plain right Afcenfion right Angles right Line Scale Secant SECT Ship Side BC Sliding Rule South Spherical Triangles Stile Stile's height Sub-ftile Sun's theſe thofe thro Triangle ABC verfed Sine Weft whofe Complement
Δημοφιλή αποσπάσματα
Σελίδα 38 - 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 124 - As the cosine of half the sum of the two sides is to the cosine of half their difference, so is the cotangent of half the contained angle to the tangent of half the sum of the other two angles.
Σελίδα 37 - FG 5 that is in Words, half the Sum of the Legs, Is to half their Difference, As the Tangent of half the Sum of the oppofite Angles, Is to the Tangent of half their Difference : But Wholes are as their Halves ; wherefore the Sum...
Σελίδα 36 - IN a plain triangle, the fum of any two fides is to their difference, as the tangent of half the fum of the angles at the bafe, to the tangent of half their difference.
Σελίδα 87 - ... to make the heart of a spectator ache, who knows the effect and the absurdity of it, to see five horses at length drawing a plough, and that perhaps upon a rich loam, where the force required is not more than 3 cwt. He cannot but think that in such cases the first horse draws the second, the second the third, the third the fourth, the fourth the fifth, and the fifth the plough, and that in fact the principal part of the draught lies upon the first horse...
Σελίδα 119 - TWo fides and an angle oppofite to one of them being given, To find the third fide and either of the other angles.
Σελίδα 38 - FG ; that is in Words, half the Sum of the Legs is to half their Difference, as the Tangent of half the Sum of the oppofite Angles is to the Tangent of half their Difference : But Wholes are as their Halves ; wherefore the Sum of the Legs is to their Difference, as the Tangent of half the Sum of the Angles oppofice is to the Tangent of half their Difference. j£. ED Axiom IV. -4. The Bale, or greateu Side of any $£• Plane Triangle is to the Sum of fs...