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 85
... the fame circular Parts . Let G repre fent the Zenith , A the North Pole , and D the Sun being in the Horizon : So that IGB is an Arch of the Meridian of the Place , BDF an Arch G 3 of Chap . 7 . 85 Spherical Trigonometry .
... the fame circular Parts . Let G repre fent the Zenith , A the North Pole , and D the Sun being in the Horizon : So that IGB is an Arch of the Meridian of the Place , BDF an Arch G 3 of Chap . 7 . 85 Spherical Trigonometry .
Σελίδα 86
... Meridian of the Place , BDF an Arch of the Horizon , FEC an Arch of the Circle described about the Sun , CAH an Arch of the Meridian of the Sun , HLI an Arch of the Equinoctial . Then do thefe five Arches retain the Conditions required ...
... Meridian of the Place , BDF an Arch of the Horizon , FEC an Arch of the Circle described about the Sun , CAH an Arch of the Meridian of the Sun , HLI an Arch of the Equinoctial . Then do thefe five Arches retain the Conditions required ...
Σελίδα 145
... Meridian Altitude , and there remain the natural Sines of the Altitudes fought . If this Difference cannot be fubtracted from the Sine of the Meridian Altitude , it argues the Sun hath no Altitude above the Horizon ; in this Cafe ...
... Meridian Altitude , and there remain the natural Sines of the Altitudes fought . If this Difference cannot be fubtracted from the Sine of the Meridian Altitude , it argues the Sun hath no Altitude above the Horizon ; in this Cafe ...
Σελίδα 146
... Meridian Altitude is 61 ° 58 ' And its natural Sine is From which fubtract Remains 8826743 764290 the Difference found . 8062453 the nat . Sine of 53 ° 44 ′ The Summer Altitude for the Hours 10 and 2 . The Winter Meridian Altitude is 14 ...
... Meridian Altitude is 61 ° 58 ' And its natural Sine is From which fubtract Remains 8826743 764290 the Difference found . 8062453 the nat . Sine of 53 ° 44 ′ The Summer Altitude for the Hours 10 and 2 . The Winter Meridian Altitude is 14 ...
Σελίδα 147
... Meridian Altitude 2588190 Refts 1640629 the nat . Sine of 9 ° 26 ' , Sammer Altitude for 5 in the Morning , or 7 at Night . The Summer Meridian Altitude as before 8826743 The former Difference Refts the natural Sine of 27 ° 22 ′ 4228819 ...
... Meridian Altitude 2588190 Refts 1640629 the nat . Sine of 9 ° 26 ' , Sammer Altitude for 5 in the Morning , or 7 at Night . The Summer Meridian Altitude as before 8826743 The former Difference Refts the natural Sine of 27 ° 22 ′ 4228819 ...
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...