An Introduction to the Theory and Practice of Plain and Spherical Trigonometry: And the Stereographic Projection of the Sphere : Including the Theory of Navigation ...Longman, Rees, Orme, Brown, and Green, 1826 - 442 σελίδες |
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Σελίδα xxi
... DOUBLE ARCS and of HALF ARCS , with formulæ , & c . 106 to 111 3. General properties of the sines , tangents , & c . of the SUMS , and of the DIFFERENCES of ARCS , including a great variety of formulæ • 111 to 118 4. General properties ...
... DOUBLE ARCS and of HALF ARCS , with formulæ , & c . 106 to 111 3. General properties of the sines , tangents , & c . of the SUMS , and of the DIFFERENCES of ARCS , including a great variety of formulæ • 111 to 118 4. General properties ...
Σελίδα xxv
... double the height of the observed object , is to the sine of double the angle of elevation MISCELLANEOUS PROPOSITIONS , & c . Prop . 1. Of the FRENCH division of the circle , and to turn . French degrees , minutes , & c . into English ...
... double the height of the observed object , is to the sine of double the angle of elevation MISCELLANEOUS PROPOSITIONS , & c . Prop . 1. Of the FRENCH division of the circle , and to turn . French degrees , minutes , & c . into English ...
Σελίδα 15
... double it , and subtract 9.69897 from the product . Required the natural versed || Required the natural versed sine of 65 ° .45 ' . · Radius = 1 Nat . cosine 65 ° .45 ′ 41072 versed sine 65 ° .45 ' . 58928 Required the logarithm ...
... double it , and subtract 9.69897 from the product . Required the natural versed || Required the natural versed sine of 65 ° .45 ' . · Radius = 1 Nat . cosine 65 ° .45 ′ 41072 versed sine 65 ° .45 ' . 58928 Required the logarithm ...
Σελίδα 29
... double to an angle at the circumference when they both stand on the same arc . ( R ) Every angle in a semicircle is a right angle . BOOK II . CHAPTER I. DEFINITIONS OF PLANE TRIGONOMETRY , CHAP V. 29 GEOMETRICAL DEFINITIONS , & c .
... double to an angle at the circumference when they both stand on the same arc . ( R ) Every angle in a semicircle is a right angle . BOOK II . CHAPTER I. DEFINITIONS OF PLANE TRIGONOMETRY , CHAP V. 29 GEOMETRICAL DEFINITIONS , & c .
Σελίδα 30
... double the radius . Thus AD and вb are diameters , and are each of them double of AC or of bc . ( F ) The exact ratio between H Chord Radius A Co Trang ECo - Sin Sine Co - Sin ver GSin D T Tangent the radius and the circumference of a ...
... double the radius . Thus AD and вb are diameters , and are each of them double of AC or of bc . ( F ) The exact ratio between H Chord Radius A Co Trang ECo - Sin Sine Co - Sin ver GSin D T Tangent the radius and the circumference of a ...
Συχνά εμφανιζόμενοι όροι και φράσεις
acute angle CAB Answer apparent altitude azimuth base centre circle co-tangent compasses complement construction cosec cosine degrees diff difference of latitude difference of longitude draw ecliptic equator Euclid find the angle formulæ given side greater Greenwich Hence horizon horizontal parallax hypoth hypothenuse less line of numbers line of sines log sine measured meridian miles moon's N.sine N.cos natural number Naut Nautical Almanac noon North oblique observed obtuse opposite angle parallax parallel perpendicular plane sailing Plate pole prime vertical PROPOSITION quadrant Rad x sine rad2 radius rhumb line right angles right ascension right-angled spherical triangle RULE scale of chords SCHOLIUM secant side AC sine A sine sine BC Sine Co-sine sphere spherical angle spherical triangle ABC Spherical Trigonometry star star's subtract sun's declination supplement tables tang tangent of half three angles three sides Trigonometry true altitude versed sine
Δημοφιλή αποσπάσματα
Σελίδα 21 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Σελίδα 2 - And if the given number be a proper vulgar fraction ; subtract the logarithm of the denominator from the logarithm of the numerator, and the remainder will be the logarithm sought ; which, being that of a decimal fraction, must always have a negative index.
Σελίδα 28 - The CO-SINE of an arc is the sine of the complement of that arc as L.
Σελίδα 107 - 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 31 - An angle at the circumference of a circle is measured by half the arc that subtends it. Let BAC be an angle at the circumference : it has for its measure half the arc "BC, which subtends it.
Σελίδα 136 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Σελίδα 258 - The HORIZON is a great circle which separates the visible half of the heavens from the invisible ; the earth being considered as a point in the centre of the sphere of the fixed stars.
Σελίδα 28 - The SECANT of an arc, is a straight line drawn from the center, through one end of the arc, and extended to the tangent which is drawn from the other end.
Σελίδα 27 - The sine, or right sine, of an arc, is the line drawn from one extremity of the arc, perpendicular to the diameter passing through the other extremity. Thus, BF is the sine of the arc AB, or of the arc BDE.