Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	draw_v	line_n	perpendicular_a	3,095	5	14.0786	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A64580	The whole art of reflex dialling shevving the vvay to make all manner of dials which shall shew the houre by a spot of light reflected from a glasse upon any cieling whether it be flat or curved, or any other way irregular. As also upon any other object whatsoever, and whether the glasse be plain, or convex, as likewise whether it lie in the plain of the horizon, or oblique unto it. Together with all necessary furniture belonging thereunto. All performed by an easie instrument fitted, with lines to that purpose. Published by Anthony Thompson.	Thompson, Anthony, d. 1665 or 6.	1658 (1658)	Wing T998A; ESTC R219276	6,125	21

the thicknesse of your Instrument so that the hollow part of the Ruler encompassing the socket the fiducial edge may passe through the Center of your Glasse which you may marke with a little speck of ink till your Dial is done The houres are to be drawn in this manner First limit the Horizon if your Glasse lye oblique to it to the end the line be not extended where the Sun can never shine This work is easily done if the roof be flat by finding onely two points thus Place your Instrument as before and slip the moveable socket to 0 deg 0 min. then hang up a perpendicular threed in any part of the roof that it may fall upon the Horizon then putting your Instrument gently to the threed observe with your eye where the fiducial edge of the socket is reflected through the Center of your Glasse and there make a mark by a slipping knot or any other way you please then holding a thread upon the Center of your Glasse gently extend it by the former mark till it come to the Cieling and there make a mark for that shall be one point of your Horizon reflected repeat this work as oft as you please so shall you have as many points as you desire through which draw a line that makes no angles which shall be the reflected Horizon Go now to your Table of distances from the East and first set off the six of Clock line in this manner Extend a threed infinitely that may passe through the Center of your Glasse and the six of Clock mark in your Horizontal Circle then in the reflected Horizon hold up a perpendicular thread with a plummet at the end that may just touch your other threed and in the reflected Horizon make a mark Do thus for all the other distances according to your Table and make several marks Then lastly go to your Table for the Tropick of Cancer and in the mark in your Circle belonging to every hour place your Instrument and move the socket in the upright ruler to the degree of Altitude belonging to that hour and marked in the Table and with your eye project it by a threed hung up any where with a slipng knot in the same manner you did your reflected Horizon and where a threed extended from the Center of the Glasse touching the Cieling that is the point for that hour and a line drawn from the point to its correpspondent in the Horizon shall represent the line where the reflected spot of light will be for all the yeer Do this for all the rest Chap. 4. IN this manner may the furniture of Dialls be easily put on viz. the Parallels of Declination of Altitude of Azimuth points of the Compasse proportions of the shadowes to the Gnomons and the like which every mans industry will easily perform Chap. 5. How to performe all the fore-going precepts without any projection by the eye FOrasmuch as the finding the reflection of the socket h i through the Center of the Glasse and after that the projection of the necessary points may seem difficult to some not used thereunto though in it self it be easie I have added this Chapter whereby the help of an instrument A B Let the perpendicular ruler of your projecting Instrument C M be placed within the room and applyed to that Azimuth to which you desire to project the correspondent hour and then by help of your plummet B C observe what inclination your Glasse hath to the Horizon in that Azimuth double that and adde it to your tabular Altitude and to that degree remove your sight then a threed drawn thereby from the Center of the Glasse shall give you the point desired in the roof Example In the latitude of 52. 15 in the Tropick of Cancer I find the Suns Azimuth 15 deg and the Altitude in our Horizon 18 d. 30′ But by a plumb line B C I find the Glasse in that Azimuth to incline to the Horizon 5 d. 00′ I say if to 18 d. 30′ the Altitude in our Horizon I adde 10 d. 00′ the double of the inclination of the Glasse and to the Altitude viz. 28 d. 30′ I remove the sight h D i and from the Center of the Glasse through the point D I draw a threed that shall shew the point upon the roof But because the Diameter of the Glasse is commonly little and consequently the inclination not accurately to be taken you must either continue the plain of your Glasse or work by this proportion As the Radius is to the tangent of the greatest Inclination So is the Cosine of the Ark comprehended between that and the Azimuth in which you seek the Inclination to the tangent of the Inclination sought E B A D C 〈…〉 ED the greatest inclination DC the Ark comprehended between the two Azimuths BC the inclination sought A the common intersection of the Horizon of the plain and of the place the proportion is plain as AD Radius is to DE tangent So is AC the Cosine of DC to BC a tangent But here it is necessary that the Glasse be first fixed at a given angle FINIS A general and most easie way to project houre lines on all kinds of superficies without any knowledge how they are situated in respect of Declination or Inclination 1. LEt the Gnomon being first sharpned with a point be shaped and fastned in such manner that it may no ways hinder either the Draught of the Horizontal line or the point of the shadow from having free accesse to the Dial at all times of the yeare 2 Draw a Horizontal line by help of the Semicircle in a true levell both in regard of it self also to the point of the Gnomon through the whole superficies on which the Dial is to be described and if the superficies be very much inclined to the Horizon so that it will not receive the horizontal line upon it you must set up some board or such like upon which for a time you are to inscribe the Horizontal line and by help of which the houre lines are to be projected upon the superficies 3 Observe the point of the shadow of the Gnomon and the Suns Altitude at the same instant of time 4 By the Altitude observed compute the Azimuth of the Sun from the Meridian 5 The same Azimuth must be projected upon the Horizontal line by help of a perpendicular threed either applyed to the point of the Gnomon or else covering to your sight the point of the Gnomon and shadow both together and with the same view cutting thorough the Horizontal line observe exactly where it then cuts for that same section shall be the Azimuth projected upon the Horizontal line 6 Let any kind of Plaine board or Past-board be now applyed to the Horizontal line which must also touch the point of the Gnomon and consequently shall therefore exactly agree with the Plane of the Horizon upon which Plane the point of the Gnomon is