An introduction to plain trigonometry, with its application to heights and distancesM. Heavisides, for the author, 1792 - 99 Seiten |
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Seite 33
... Hypothenuse be made Radius , each Leg will be the Sine of its oppofite Angle . Plate 1. Fig . 1. Where it is evident ( from Definition 7 ) that A B is the Sine of the Arch A C , and BC the Sine of the Arch C D. Rule * As any one Side ...
... Hypothenuse be made Radius , each Leg will be the Sine of its oppofite Angle . Plate 1. Fig . 1. Where it is evident ( from Definition 7 ) that A B is the Sine of the Arch A C , and BC the Sine of the Arch C D. Rule * As any one Side ...
Seite 46
... AC Secant . RULE * As the Radius Is to the Base So is Tang . of the Angle oppofite to the Perpend To the Perpend . and As the Radius Is to the Base So is the Secant of the fame Z To the Hypothenuse . And the contrary . DEMONSTRATION ...
... AC Secant . RULE * As the Radius Is to the Base So is Tang . of the Angle oppofite to the Perpend To the Perpend . and As the Radius Is to the Base So is the Secant of the fame Z To the Hypothenuse . And the contrary . DEMONSTRATION ...
Seite 54
... Hypothenuse . As Tang . of the Z A 33 ° 45 ' Is to the Perpend . 2778 2 ° 443709 9 * 824892 2 ° 443709 So is Secant ... AC 500 , to find the Angles and Perpendicular . Logarithmetically . 500 415.8 B PA LOGARITHMETICALLY . Both the Base ...
... Hypothenuse . As Tang . of the Z A 33 ° 45 ' Is to the Perpend . 2778 2 ° 443709 9 * 824892 2 ° 443709 So is Secant ... AC 500 , to find the Angles and Perpendicular . Logarithmetically . 500 415.8 B PA LOGARITHMETICALLY . Both the Base ...
Seite 61
... Hypothenuse AC ind the Angle A 29 ° 57 ' , to find the and Perpendicular . Ll A 29.57 63 B LOGARITHMETICALLY . ICA I The Hypothenufe and Angles are here given to find the Bafe and Perpendicular . Turn to Plate 3 , and you will foon ...
... Hypothenuse AC ind the Angle A 29 ° 57 ' , to find the and Perpendicular . Ll A 29.57 63 B LOGARITHMETICALLY . ICA I The Hypothenufe and Angles are here given to find the Bafe and Perpendicular . Turn to Plate 3 , and you will foon ...
Seite 68
... A C 180 and Angle A 450 to find the Perpendicular and Bafe . Ans . The Perpend . 127 ° 3 and Base 127 ° 3 2. There ... Hypothenuse , Ans . The Per . 33 ° 48 and Hypoth . 66:97 . 4. Required the Angles and Base of the right angled ...
... A C 180 and Angle A 450 to find the Perpendicular and Bafe . Ans . The Perpend . 127 ° 3 and Base 127 ° 3 2. There ... Hypothenuse , Ans . The Per . 33 ° 48 and Hypoth . 66:97 . 4. Required the Angles and Base of the right angled ...
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An Introduction to Plain Trigonometry, with Its Application to Heights and ... Richard Cockrel Keine Leseprobe verfügbar - 2018 |
An Introduction to Plain Trigonometry, with Its Application to Heights and ... Richard Cockrel Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
A B C ABC are given alfo angled plain Triangle angled Triangle ABC Angles and Hypothenufe Arch D E Bafe and Hypothenufe becauſe bifect Cafe Centre Chord of 60 Compaffes confequently defcribe an Arch defcribe another Arch Diſtance draw A B fame fhall find the Angles find the Bafe find the Perpendicular firſt Foot fubtracted from 90 fuch fuppofe GEOMETRICALLY given right Line given the Hypothenufe gives the greater gives the leffer half the Difference half the Sum Houſe Hypoth Hypothenufe AC laſt lay off thereon lefs Line of Chords LOGARITHMETICALLY meaſured Number of Degs oblique angled plain oppofite Angle Parallelogram Perpend Perpendicu plain Triangle ABC Point of Interfection Proportion PROPOSITION Queſtion Radius 90 refpectively required the Angles right angled Triangle Scale of equal Secant Sect Side A B 70 Side and Angles Side BC 120 Sine Tang Tangent Trigono Turn to Plate
Beliebte Passagen
Seite 60 - As the base or sum of the segments Is to the sum of the other two sides, So is the difference of those sides To the difference of the segments of the base.
Seite 8 - If equal quantities be added to equal quantities, the sums will be equal.
Seite 75 - I measured a base of 500 yards in a straight line close by one side of it ; and at each end of this line I .found the angles subtended by the other end and a tree, close to the bank on the other side of the river, to be 53° and 79° 12'.
Seite 68 - What is the perpendicular height of a hill whose angle of elevation, taken at the bottom of it, was 46° ; and 100 yards farther off, on a level with the bottom of it, the angle was 31° ? Ans., 143.14 yards.
Seite 73 - I measured out for a base 400 yards in a right line by the side of the river, and found that the two angles, one at each end of this line, subtended by the other end and the house, were 68° 2
Seite 73 - Being on one side of a river and wanting to know the distance to a house, which stood on the other side, I measured 200 yards in a right line by the side of the river, and found that the two angles at each end of this line formed by the other end and the house were 73° 15' and 68° 2'; what was the distance between each station and the house ? Ans.
Seite 57 - As the sum of the two sides Is to their difference, So is the tan of half the sum of the unknown angles To the tan of half the difference of the unknown angles. And this tan half difference added to the half sum of two unknown angles gives the greater angle, and subtracted gives the less angle. Taking the example already given (fig. 29) : — AC + AD = 50 + 40...
Seite 17 - Triangles on the fame Bafe, and between the fame Parallels, are equal ; becaufe they are Half the circumfcribing Parallelograms.
Seite 70 - I meafured from its bottom a diftance of 40 feet, and then took the angle formed by the plane and a line drawn to the top 41"; and going 'on in the fame...
Seite 40 - DE, and ercdl the perpendicular DF ; which, it is evident, will be the tangent, and AF the fecant of the arc DE, or angle A, to the radius AD.