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end_n draw_v line_n perpendicular_a 3,095 5 14.0786 5 true
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ID Title Author Corrected Date of Publication (TCP Date of Publication) STC Words Pages
A26045 Speculum nauticum a looking glasse for sea-men : wherein they may behold a small instrument called the plain scale whereby all questions nautical and propositions astronomical are very easily and demonstratively wrought ... / by Iohn Aspley. Aspley, John. 1647 (1647) Wing A4011; ESTC R27669 26,980 68

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angles in the point A. Diameter Circuli or the Diameter of a Circle is a right Line drawne thorow the Centre of any circle in such sort that it may divide the Circle into two equall parts as you may see the line B. A. D. is the Diameter of the Circle B. C. D. E. because it passeth thorow the Centre A. and the two ends therof do divide the Circle into two equall parts in the two extrems B. D making the semicircle B. C. D. equall unto the semicircle D. E. B. Semidiameter circuli or the Semidiameter of a Circle is halfe of the Diameter and is contayned betwixt the Centre and the one side of the Circle as the Line A D in the Semidiameter of the Circle B C D E. Semi-circulus or a Semi-circle is the one halfe of a Circle drawne upon his Diameter and is contained upon the Superficies or Surface of the Diameter as the Semicircle B C D which is halfe of the Circle B C D E and is contayned above the Diameter B A D. Quadrans circuli is the fourth part of a Circle and is contayned betwixt the Semidiameter of the Circle and a line drawn Perpendicular unto the Diameter of the same Circle from the Centre thereof dividing the Semicircle into two equall parts of the which parts the one is the quadrant or fourth part of the same Circle As for example the Diameter of the Circle B C D E is the line B A D dividing the Circle into two equall parts then from the Centre A raise the Perpendicular A C dividing the Semicircle likewise into two equall parts so as A B C or A C D the quasired CHAP. II. The manner how to raise a Perpendicular from the midle of a Line given DRaw first a ground line whereupon you would have a Perpendicular raised then open your Compasses unto any distance so it exceed not the end of your line placing one foot of the said Compasses in the point from whence the Perpendicular is to be raised and with the other foot make a mark in the line on both sides then removing your Compasses unto any other distance that is greater and set one foot therof in one of the marks and with the other foot make a mark over the middle point then with the same distance of your compasse set one foot in the other mark upon the Line and with the other foot make another arch of a Circle over the middle point so that it may crosse the first arch and from the meeting of these two arches draw a right Line unto the middle point from which the Perpendicular was to be raised which Line shall be the Perpendicular desired Example suppose your Base or ground Line wherupon a Perpendicular is to be raised by the Line F L K and from L the Perpendicular is to be raised set one foot of your Compasses in the point L and with the other make the marks G and M on both sides of the point L then opening your Compasses wider set one foot in the point M and with the other draw the arch S over the point L then with the same distance of your Compasses set one foot in G and with the other make the arch R. crossing the arch S. in the point T. then from T. draw the Line T. L. which Line is Perpendicular unto the Line F. L. K. from the point L which is the Perpendicular desired CHAP. III. To let a Perpendicular fall from any Point assigned unto the middle of a Line LEt the line whereupon you would have a Perpendicular let fall be the Line L F K and the Point assigned to be the point T from whence you would have a Perpendicular let fall upon the Line F L K first set one foote of your Compasses in T and open your Compasses unto any distance so that it be more than the distance T L which here wee suppose to bee the distance T M then make in the Line F L K the marks G and M then with your Compasses take the one halfe of G M which is in the point L then from L draw a Line unto the point T so the Line T L shall be the Perpendicular which was desired to be let fall from the assigned point T unto the middle of the Line F L K. CHAP. IV. To rayse a Perpendicular upon the end of a Line SUppose the Line whereupon you would have a Perpendicular raysed be the Line F L K and from the point F a Perpendicular is to be raysed first open your Compasses unto any distance which here we put to be the distance F G set one foot of your compasses in the point F and with the other draw the arch D E G then set one foote of your Compasses in the point G and with the other draw the arch E then placing one point of your Compasses in F with the other draw the arch D B then place your Compasses in D and with the same distance draw the arch A cutting the arch D B in C then draw a Line from C unto the end of the Line F L K unto the assigned point F so shall the Line G F be a Perpendicular raysed from the end of the Line F L K and from the assigned point F. CHAP. V. To let a Perpendicular fall from any point assigned unto the end of a Line LEt the Line F L K bee the Base or ground Line and from the point I a Perpendicular is to bee let fall upon the end of the Line K first from the assigned point I draw a Line unto any part of the Base which shall be the Line IHM then finde the middle of the Line IM which is at H place therefore one foote of your Compasses in the point H and extend the other unto I with which distance draw the arch INK upon the Centre H cutting the Base or ground-line in the point K then draw the Line KI which Line shall be the Perpendicular desired NOW I doubt not but you understand the way to let fall or to rayse any manner of Perpendicular Line eyther from or upon any part of a Line therefore now I intend to proceede unto the maine point here aymed at which is to declare and make known unto you the several operations performed by the plain Scale which though it be in use with very few yet it is most necessary with Sea-men because all questions in Navigation are thereby easily and plainly wrought And also all questions in Astronomy belonging unto the expert and industrious Sea-men may both speedily and easily be wrought by the same Scale in regard whereof I have declared in this little Book that knowledge which God hath beene pleased to bestow upon me concerning the necessary use and practice therof hoping that you will as kindly accept it as it is freely offered unto your courteous considerations The figure of the plaine Scale CHAP. VI Of the description of the Scale THis Scale usually is