The Theory and Practice of Surveying: Containing All the Instructions Requisite for the Skilful Practice of this ArtE. Duyckinck, 1811 - 508 páginas |
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Página 45
... half , third , fourth , & c . part . Note , Though these postulates are not always quoted the reader will easily perceive where , and in what sense they are to be understood . AXIOMS or self - evident TRUTHS . 1. Things that are equal ...
... half , third , fourth , & c . part . Note , Though these postulates are not always quoted the reader will easily perceive where , and in what sense they are to be understood . AXIOMS or self - evident TRUTHS . 1. Things that are equal ...
Página 51
... half the arc it subtends or stands on . Fig . 26 . Cor . 2. Hence all angles at the circumference of a circle which stands on the same chord as AB , are equal to each other , for they are all measured by half the arc they stand on , viz ...
... half the arc it subtends or stands on . Fig . 26 . Cor . 2. Hence all angles at the circumference of a circle which stands on the same chord as AB , are equal to each other , for they are all measured by half the arc they stand on , viz ...
Página 52
... half the arc AB , but as the arc AB is less than a semicircle , therefore half the arc AB , or the angle ADB is less than half a semi- circle , and consequently less than a right angle . Fig . 27 . Cor . 4. An angle in a segment less ...
... half the arc AB , but as the arc AB is less than a semicircle , therefore half the arc AB , or the angle ADB is less than half a semi- circle , and consequently less than a right angle . Fig . 27 . Cor . 4. An angle in a segment less ...
Página 53
... half the chord of 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. ) therefore the corollary is plain . THEO . X. PL . 1. fig . 30 . In any triangle ABD , the ...
... half the chord of 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. ) therefore the corollary is plain . THEO . X. PL . 1. fig . 30 . In any triangle ABD , the ...
Página 54
... half the arc BKD , ( by cor . 1. theo . 7. ) viz . the chord of BK is the measure of the angle BAD ; therefore ( by cor . to the last ) BE the half of BD is the sine of BAD : the same way may be proved that half of AD is the sine of ABD ...
... half the arc BKD , ( by cor . 1. theo . 7. ) viz . the chord of BK is the measure of the angle BAD ; therefore ( by cor . to the last ) BE the half of BD is the sine of BAD : the same way may be proved that half of AD is the sine of ABD ...
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Términos y frases comunes
acres altitude Answer arch azimuth base bearing blank line centre chains and links chord circle circumferentor Co-sec Co-tang column compasses contained decimal difference distance line divided divisions draw east Ecliptic edge feet field-book figures fore four-pole chains geom given number half the sum Horizon glass hypothenuse inches instrument Lat Dep Lat latitude length logarithm measure meridian distance multiplied natural co-sine natural sine needle Nonius number of degrees object observed off-sets opposite parallel parallelogram pegs perches perpendicular plane pole pole star Portmarnock PROB protractor Quadrant quotient radius right angles right line scale of equal SCHOLIUM screw Secant sect Sextant side sights square station stationary distance subtract Sun's survey taken Tang tangent theo theodolite trapezium triangle ABC trigonometry two-pole chains vane versed sine vulgar fraction whence
Pasajes populares
Página 38 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Página 25 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, &c.
Página 197 - RULE. From half the sum of the three sides subtract each side severally.
Página 106 - 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.
Página 27 - The VERSED SINE of an arc is that part of the diameter which is between the sine and the arc. Thus BA is the versed sine of the arc AG.