Selected quad for the lemma: day_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
day_n	hour_n	march_n	minute_n	4,990	5	12.3227	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A64223	The semicircle on a sector in two books. Containing the description of a general and portable instrument; whereby most problems (reducible to instrumental practice) in astronomy, trigonometry, arithmetick, geometry, geography, topography, navigation, dyalling, &c. are speedily and exactly resolved. By J. T.	Taylor, John, 1666 or 7-1687.	1667 (1667)	Wing T533B; ESTC R221720	52,688	153

line of seconds continued unto 60 and marked at the end Se. Next to the outward edge on the fixed and movable piece which is best discerned when those pieces are opened to the full length is a line of Meridians divided to 85 whose use is for Navigation in describing Maps or Charts c. In the vacant spaces you may have a line of chords sines and tangents to any Radius the space will bear and what other any one thinks best of as a line of latitudes and hours c. On the proportional side of the loose piece are lines for measuring all manner of solids as Timber Stone c. likewise for gaging of Vessels either in Wine or Ale measure On the outward ledge of the movable and fixed piece both which in use must be stretched out to the full length is a line of artificial numbers sines tangents and versed sines The first marked N the second S the third T the fourth VS On the inward ledge of the movable piece is a line of 12 inches divided into halfs quarters half-quarters Next to that is a prick'd line whose use is for computing of weight and carriages Lastly a line of foot measure or a foot divided into ten parts and each of those subdivided into ten or twenty more On the inward ledge of the loose piece you may have a line of circumference diameter square equal and square inscribed There will still be requisite sights a thread and plummet And if any go to the price of a sliding Index to find the shadow from the plains perpendicular in order to taking a plains declination and have a staff and a ballsocket the Instrument is compleated with its furniture Proceed we now to the uses Onely note by the way that Mr. Brown hath for conveniency of carrying a pair of Compasses Pen Ink and Pencil contrived the fixed piece and movable both to be hollow and then the pieces that cover those hollows do one supply the place of the loose piece for taking altitudes the other being a sliding rule for measuring solids and gaging Vessels without Compasses CHAP. II. Some uses of the quadrantal side of the Instrument PROBL. 1. To find the altitude of the Sun or any Star HAng the thread and plummet upon the pin at the beginning of the line of sines on the fixed piece and having two sights in two holes parallel to that line raise the end of the fixed piece toward the Sun until the rayes pass through the sights but when the Sun is in a cloud or you take the altitude of any Star look along the outward ledge of the fixed piece until it be even with the middle of the Sun or Star then on the limb the thread cuts the degree of altitude if you reckon from 0 60 on the loose piece toward the head of the movable piece PROBL. 2. The day of the Moneth given to find the Suns place declination ascensional difference or time of rising and setting with his right ascension The thread laid to the day of the Moneth gives the Suns place in the line of signs reckoning according to the order of the Moneths viz. forward from March the 10th to June then backward to December and forward again to March 10. In the limb you have the Suns declination reckoning from 60 0 on the movable piece towards the head for North toward the end for South declination Again on the line of right ascensions the thread shews the Suns right ascension in degrees or hours according to the making of your line counting from Aries toward the head and so back again according to the course of the signs unto 24 hours or 360 degrees Lastly on the line of hours you have the time of Sun rising and setting which turned into degrees for the time from six gives the ascensional difference Ex. gr in lat 52. deg 30 min. for which latitude I shall make all the examples The 22 day of March I lay the thread to the day in the Moneths and find it cut in the Signs 12 deg 20 min. for the Suns place on the limb 4 deg 43 min. for the Suns declination North. In the line of right ascensions it gives 46 min. of time or 11 deg 30 min. of the circle Lastly on the line of hours it shews 28 min. before six for the Suns rising or which is all 7 deg for his ascensional difference PROBL. 3. The declination of the Sun or any Star given to find their amplitude Take the declination from the scale of altitudes with this distance setting one point of your Compasses at 90 on the line of Azimuth apply the other point to the same line it gives the amplitude counting from 90 Ex. gr at 10 deg declination the amplitude is 16 deg 30 min. at 20 deg declination the amplitude is 34 deg PROBL. 4. The right ascension of the Sun with his ascensional difference given to find the oblique ascension In Northern declination the difference betwixt the right ascension and ascensional difference is the oblique ascension In Southern declination take the summ of them for the oblique ascension Ex. gr at 11 deg 30 sec. right ascension and 6 deg 30 sec. ascensional difference In Northern declination the oblique ascension will be 5 deg in Southern 18 deg PROBL. 5. The Suns altitude and declination or the day of the Moneth given to find the hour Take the Suns altitude from the Scale of altitudes and laying the thread to the declination in the limb or which is all one to the day in the Moneths move one point of the compasses along the line of hours on that side the thread next the end until the other point just touch the thread then the former point shews the hour but whether it be before or after noon is left to your judgment to determine Ex. gr The 22 day of March or 4 deg 43 min. North declination and 20 deg altitude the hour is either 47 minutes past 7 in the morning or 13 minutes past 4 afternoon PROBL. 6. The declination of the Sun or day of the Moneth and hour given to find the altitude Lay the thread to the day or declination and take the least distance from the hour to the thread this applyed to the line of altitudes gives the altitude required Ex. gr The 5 day of April or 10 deg declination North at 7 in the morning or 5 afternoon the altitude will be 17 deg 10 sec. and better PROBL. 7. The declination and hour of the night given to find the Suns depression under the horizon Lay the thread to the declination on the limb but counted the contrary way viz. from 60 0 on the movable piece toward the head for Southern and toward the end for Northern declination This done take the nearest distance from the hour to the thread and applying it to the line of altitudes you have the degrees of the Suns depression Ex. gr at 5 deg Northern declination 8 hours afternoon the depression

is 13 deg 30 min. PROBL. 8. The declination given to find the beginning and end of twilight or day-break Lay the thread to the declination counted the contrary way as in the last Problem and take from your Scale of altitudes 18 deg for twilight and 13 deg for day-break or clear light with this run one point of the Compasses along the line of houres on that side next the end until the other will just touch the thread and then the former point gives the respective times required Ex. gr At 7 deg North declination day breaks 8 minutes before 4 but twilight is 3 houres 12 minutes in the morning or 8 hours 52 minutes afternoon PROBL. 9. The declination and altitude of the Sun or any Star given to find their Azimuth in Northern declination Lay the thread to the altitude numbred on the limb of the moveable piece from 60 0 toward the end and when occasion requires continue your numbring forward upon the loose piece and take the declination from your line of altitude with this distance run one point of your Compasses along the line of Azimuths on that side the thread next the head until the other just touch the thread then the former point gives the Azimuth from South Ex. gr at 10 deg declination North and 30 deg altitude the Azimuth from South is 64 deg 40 min. PROBL. 10. The Suns altitude given to find his Azimuth in the aequator Lay the thread to the altitude in the limb counted from 60 0 on the loose piece toward the end and on the line of Azimuths it cuts the Azimuth from South Ex. gr at 25 deg altitude the Azimuth is 53 deg At 30 deg altitude the Azimuth is 41 deg 30 min. fere PROBL. 11. The declination and altitude of the Sun or any Star given to find the Azimuth in Southern declination Lay the thread to the altitude numbred on the limb from 60 0 on the moveable piece toward the end and take the declination from the Scale of altitudes then carry one point of your Compasses on the line of Azimuths on that side the thread next the end until the other just touch the thread which done the former point gives the Azimuth from South Ex. gr at 15 deg altitude and 6 deg South declination the Azimuth is 58 deg 30 min. PROBL. 12. The declination given to find the Suns altitude at East or West in North declination and by consequent his depression in South declination Take the declination given from the Scale of altitudes and setting one point of your Compasses in 90 on the line of Azimuths lay the thread to the other point on that side 90 next the head on the limb it cuts the altitude counting from 60 0 on the moveable piece Ex. gr at 10 deg declination the altitude is 12 deg 40 min. PROBL. 13. The declination and Azimuth given to find the altitude of the Sun or any Star Take the declination from the Scale of altitudes set one point of your Compasses in the Azimuth given then in North declinanation turn the other point toward the head in South toward the end and thereto laying the thread on the limb you have the altitude numbring from 60 0 on the moveable piece toward the end Ex. gr At 7 deg North declination and 48 deg Azimuth from South the altitude is 35 deg but at 7 deg declination South and 50 deg Azimuth the altitude is onely 18 deg 30 min. PROBL. 14. The altitude declination and right ascension of any Star with the right ascension of the Sun given to find the hour of the night Take the Stars altitude from the Scale of altitudes and laying the thread to his declination in the limb find his hour from the last Meridian he was upon as you did for the Sun by Probl. 5. If the Star be past the South this is an afternoon hour if not come to the South a morning hour which keep Then setting one point of your Compasses in the Suns right ascension numbred upon the line twice 12 or 24 next the outward ledge on the fixed piece extend the other point to the right ascension of the Star numbred upon the same line observing which way you turned the point of your Compasses viz. toward the head or end With this distance set one point of your Compasses in the Stars hour before found counted on the same line and turning the other point the same way as you did for the right ascensions it gives the true hour of the night Ex. gr The 22 of March I find the altitude of the Lions heart 45 deg his declination 13 d. 40 min. then by Probl. 5. I find his hour from the last Meridian 10 houres 5 min. The right ascension of the Sun is 46 m. of time or 11 d. 30 m. of the Circle the right ascension of the Lions heart is 9 hour 51 m. fere of time or 147 deg 43 m. of a circle then by a line of twice 12 you may find the true hour of the night 7 hour 13 min. PROBL. 15. The right ascension and declination of any Star with the right ascension of the Sun and time of night given to find the altitude of that Star with his Azimuth from South and by consequent to find the Star although before you knew it not This is no more than unravelling the last Problem 1 Therefore upon the line of twice 12 or 24 set one point of your Compasses in the right ascension of the Star extending the other to the right ascension of the Sun upon the same line that distance laid the same way upon the same line from the hour of the night gives the Stars hour from the last Meridian he was upon This found by Probl. 5. find his altitude as you did for the Sun Lastly having now his declination and altitude by Probl. 8. or 10. according to his declination you will soon get his Azimuth from South This needs not an example By help of this Problem the Instrument might be so contrived as to be one of the best Tutors for knowing of the Stars PROBL. 16. The altitude and Azimuth of any Star given to find his declination Lay the thread to the altitude counted on the limb from 60 0 on the moveable piece toward the end setting one point of your Compasses in the Azimuth take the nearest distance to the thread this applyed to the Scale of altitudes gives the declination If the Azimuth given be on that side the thread toward the end the declination is South when on that side toward the head its North. PROBL. 17. The altitude and declination of any Star with the right ascension of the Sun and hour of night given to find the Stars right ascension By Probl. 5. or 14. find the Stars hour from the Meridian Then on the line twice 12 or 24 set one point of your Compasses in the Stars hour thus found and extend the other to the hour of the night Upon the same line

piece to be put into the tenons as before expressed The quadrantal side of the joyned pieces is easily discerned having the names of the Moneths stamped on the movable piece and Par. Scale on the fixed piece The quadrantal side of the loose piece is known by the degrees on the inward and outward limb These directions are sufficient to instruct you how to put the Instrument together Imagining the Instrument thus put together the lines upon the quadrantal side are these First on the fixed piece next the outward limb is a line of 12 equal parts and each of those parts divided into 30 degrees marked from the end towards the head with ♈ ♉ ♊ c. representing the 12 Signs of the Zodiack the use of this line with the help of those under it was intended to find the hour of the night by the Moon The next line to this is a line of twice 12 or 24 equal parts each division whereof cuts every 15th degree of the former line and therefore if the figures were set to every 15th degree on this side the former line this second line would be useless and the former perform its office more distinctly This line was intended an assistant for finding the hour by the Moon but is very ready to find the hour by any of the fixed Stars The third line is a line of 29● equal parts serving for the dayes of the Moons age in order to find the hour of the night by the Moon But the operation is so tedious and far from exactness that I have no kindness for it and should place some other lines in the room of this and the former did I not resolve to impose upon no mans phantasie The fourth line is a line of altitudes for a particular latitude noted at the end Par. Scale c. This helpeth to find the hour and azimuth of the Sun or any fixed Star very exactly The fifth line is a line of natural sines at the beginning whereof there is a pin or else an hole to put a pin into whereon to hang the thread and plummet for taking of altitudes To this line of sines may be joyned a line of tangents to 45 degr The use of the sines alone is to work proportions in signs The use of the sines with the tangent line may be for any proportion in trigonometry but that I leave to liberty The sixth line and last on this side the fixed piece is a line of versed sines numbred from the centre at the head to 180 at the end On the quadrantal side of the movable piece the first line next the inward edge is a line of versed sines answering to that on the fixed piece The use of these versed sines is various at pleasure The second line from the inward edge is a line of hours and Azimuths serving to find the hour by the Sun or Stars or the Azimuth of the Sun or any fixed Star from the South The third and fourth lines are lines of Moneths marked with the respective names and each Moneth divided into so many parts as it contains dayes The fifth line is a line of signs marked ♈ Taurus Gemini c. each sign being divided into 30 degr and proceeding from ♈ or Aries which answers to the tenth of March in the same order as the Moneths The use of this line with help of the Moneths is to find the Suns place in the Zodiack The sixth line is a line of the Suns right ascension commonly noted by hours from 00 to 24. but better if divided by degrees or sines from 00 to 360 and both wayes proceeding backward and forward as the signs of the Zodiack or dayes of the Moneth Lastly the outward edge or limb of the movable and loose piece both is graduated unto 180 degrees or two quadrants whose centre is the pin or pin-hole before mentioned at the beginning of the sines on this side the fixed piece The perpendicular is at 0 60 upon the loose piece from whence reckoning along the outward edge of the loose piece till it intersects the produced line of sines at the end of the fixed piece you have 90 degrees Or counting from 0 60 on the loose piece and continuing it along the degrees of the outward limb of the movable piece until they intersect the produced line of sines on the fixed piece at the head you have again 90 degrees which compleat the Semicircle The use of this line is for taking of altitudes counting upon the former 90. degr when you hold the head of the fixed piece toward the Sun and numbring upon this latter when you hold which is best because the degrees are largest the end of the fixed piece toward the Sun There are other wayes of numbring these degrees for finding of the Azimuth c. which shall be mentioned in their proper places On the quadrantal side of the loose piece the inward edge or limb is graduated unto 60 degrees or twice 30 which you please whose centre is a pin at the head The use of this is to find the altitude of the Sun or any Star without thread and plummet or to perform some uses of the Cross-staff This is for large rules or instruments and therefore not illustrated here In the empty spaces upon the quadrantal side may be engraven the names of some fixed Stars with their right ascensions and declinations On the proportional side the lines issuing from the centre are the same upon the fixed and movable piece but happily transplaced thanks to the first contriver after this manner The line that lies next the inward edge on the fixed piece hath his fellow or correspondent line toward the outward edge on the movable piece by which means these lines all meeting at the centre stand all at the same angle and give you the freedom from a great deal of trouble in working proportions by sines and tangents or laying down any sine or tangent to any Radius given c. The lines issuing from the centre toward the outward edge of the movable piece whose fellow is next the inward edge of the fixed piece is a line of natural sines on the outward side marked at the end S and on the inward side a line of lines or equal parts noted at the end L the middle line serving for both of them The lines issuing from the centre next the inward edge of the movable piece whose fellows are toward the outward edge of the fixed piece are lines of natural tangents which on the outward side of the line is divided to 45 the Radius and on the inward side of the lines the middle line serving for both at a quarter of the former Radius from the centre is another Radius noted 45 at the beginning and continued to the tangent 75. These lines are noted at the end T. The use of these you will find Chap. 3,4,5 Betwixt the lines of sines and tangents both upon the fixed and movable pieces is placed a