Letter from Arthur Storer to Humphrey Babington, dated 1 October 1678

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For the Reverend D^oct
Babington of Trinity
Colidge in Cambridge
diliver
{2}

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S^ir    Returning you many thancks for your kindness I have Receved an Answer in part from M^r Newton w^ch is that he had|t|h tryed my Numbers & found them hold well: w^ch hath Incoradged me once moore to present him with with another Burd, of the same fether hatched at y^e said Time & I thinck as well Trimed & dect with fethers yett not Alltogether of so swifft a wing butt Fuly as many chaingeble Noates: I have Likewise a Great many moore such Like Tables w^ch moast of them ar by duble wayes of working w^ch I had Allmost filled a Book with w^ch: w^ch I thought once y^t it would have {comed} to M^r Newtons {wringh} & so thought affter His Examining to have brought it to perfection But now being other wayes Called of I am forced to Lett it Sleepe in Silence: Only I would desire him once moore to Looke over this Table y^t hee \may/ see whether the proportions hold good {yea} or no: as I suppose they may or Else I have spent some time therin in vane: {illeg} I suppoase I shall not Receve an answer of w^ch while I {illeg}|b|e in London for about Saterday or Munday next at the furthest I thinck that I shall take shipp & so fall doune to Graves End w^ch perhapes if an answer Come soone I may Receive it there otherwayes it may be by affter ships: Haveing no moore at p^rsent but my service to M^r Newton & my Duty to your selfe with my prayer to God for your Long Life & Comffortabe dayes I Rest your Obedient Nephew

at your Command to Serve you / Arthur Storer

London Octob^r y^e 1^th {sic} 1678:

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$\begin{array}{|c|}\hline \begin{array}{c}\text{A Table to finde the Sun or any Stars Altitude uppon Every}{\text{5}}^{\text{th}}\text{Azimuth from the East or West Eather Northward Or S}\stackrel{\_}{\text{o}}\text{wards}\\ \text{Or to finde the Sunn or any Stars Altitude by proportion uppon any point of' the Compass Or uppon any Azimuth}\\ \text{Or the Altitude \& Azimuth Given to finde the Declination For the Latitude of 51 : 52 : 53 : 54 : 55 : \&c :}\\ \phantom{0}\end{array}\\ \begin{array}{ccccc}\hfill \text{Azimuth}\hfill & \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}}& \text{Degrees of the Azimuth}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}}& \text{Azimuth}\end{array}\\ \begin{array}{cccccccccccccccccccccc}\phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& & \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \\ {\text{y}}^{\text{e}}\text{Latitude}& & 0& 5& 10& 15& 20& 25& 30& 35& 40& 45& 50& 55& 60& 65& 70& 75& 80& 85& 90& \\ \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& & \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \end{array}\\ \begin{array}{ccc}\phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{000000000000000}& \text{The Equinoctiall Altitudes uppon these Azimuth in Degrs \& min}\end{array}\\ \\ \begin{array}{cccccccccccccccccccccc}51& & \begin{array}{c}00=\underset{\phantom{·}}{00}\\ 12868\end{array}& \begin{array}{c}\phantom{0}4=\underset{\phantom{·}}{02}·\\ 12837\end{array}& \begin{array}{c}\phantom{0}8=\underset{\phantom{·}}{00}\\ 12744\end{array}& \begin{array}{c}11=\underset{\phantom{·}}{50}·\\ 12594\end{array}& \begin{array}{c}15=\underset{·}{29}\\ 12400\end{array}& \begin{array}{c}18=\underset{.·}{54}\\ 12174\end{array}& \begin{array}{c}22=\underset{.·}{03}\\ 11927\end{array}& \begin{array}{c}24=\underset{\phantom{.·}}{55}\\ 11671\end{array}& \begin{array}{c}27=\underset{\phantom{.·}}{30}\\ 11414\end{array}& \begin{array}{c}29=\underset{\phantom{.}·}{48}\\ 11167\end{array}& \begin{array}{c}31=\underset{\phantom{.·}}{49}\\ 10935\end{array}& \begin{array}{c}33=\underset{.·}{34}\\ 10723\end{array}& \begin{array}{c}\text{Deg}\phantom{00}\text{m}\hfill \\ 35=\underset{\phantom{.·}}{02}:\\ 10536\phantom{:}\end{array}& \begin{array}{c}\text{Deg}\phantom{00}\text{min}\hfill \\ 36=\underset{\phantom{.·}}{16}\\ 10375\end{array}& \begin{array}{c}\text{D}\phantom{\text{eg}}\phantom{0}\text{min}\hfill \\ 37=\underset{\phantom{.·}}{16}\\ 10240\end{array}& \begin{array}{c}\text{D}\phantom{\text{eg}}\phantom{00}\text{m}\hfill \\ 38=\underset{\phantom{.·}}{02}\\ 10136\end{array}& \begin{array}{c}\text{Deg}\phantom{00}\text{min}\hfill \\ 38=\underset{\phantom{.·}}{34}:\\ 10061\end{array}& \begin{array}{c}\text{Deg}\phantom{00}\text{min}\hfill \\ 38=\underset{.·}{54}\\ 10016\end{array}& \begin{array}{c}\text{Deg}\phantom{00}\text{min}\hfill \\ 39=\underset{\phantom{.·}}{00}\\ 10000\end{array}& \\ \phantom{0}& & & & & & & & & & & & & & & & & & & & & \\ 52& & \begin{array}{c}00=\underset{\phantom{·}}{00}\\ 12690\end{array}& \begin{array}{c}\phantom{0}3=\underset{\phantom{·}}{54}\\ 12661\end{array}& \begin{array}{c}\phantom{0}7=\underset{\phantom{·}}{43}\\ 12576\end{array}& \begin{array}{c}11=\underset{\phantom{·}}{26}\\ 12439\end{array}& \begin{array}{c}14=\underset{\phantom{·}}{57}\\ 12260\end{array}& \begin{array}{c}18=\underset{\phantom{.·}}{17}\\ 12050\end{array}& \begin{array}{c}21=\underset{\phantom{·}}{21}\\ 11820\end{array}& \begin{array}{c}24=\underset{\phantom{.·}}{08}:\\ 11580\end{array}& \begin{array}{c}26=\underset{\phantom{.·}}{40}\\ 11340\end{array}& \begin{array}{c}28=\underset{\phantom{.·}}{55}\\ 11108\end{array}& \begin{array}{c}30=\underset{\phantom{.·}}{54}\\ 10890\end{array}& \begin{array}{c}32=\underset{\phantom{.·}}{37}\\ 10699\end{array}& \begin{array}{c}34=\underset{\phantom{.·}}{06}\\ 10511\end{array}& \begin{array}{c}35=\underset{\phantom{.·}}{18}\\ 10357\end{array}& \begin{array}{c}36=\underset{\phantom{.·}}{17}\\ 10230\end{array}& \begin{array}{c}37=\underset{\phantom{.·}}{02}\\ 10130\end{array}& \begin{array}{c}37=\underset{·}{35}\\ 10058\end{array}& \begin{array}{c}37=\underset{\phantom{.·}}{54}\\ 10015\end{array}& \begin{array}{c}38=\underset{\phantom{.·}}{00}\\ 10000\end{array}& \\ \phantom{0}& & & & & & & & & & & & & & & & & & & & & \\ 53& & \begin{array}{c}00=\underset{\phantom{·}}{00}\\ 12522\end{array}& \begin{array}{c}\phantom{0}3=\underset{\phantom{·}}{46}\\ 12495\end{array}& \begin{array}{c}\phantom{0}7=\underset{\phantom{·}}{27}\\ 12416\end{array}& \begin{array}{c}11=\underset{\phantom{·}}{02}\\ 12291\end{array}& \begin{array}{c}14=\underset{\phantom{·}}{27}\\ 12126\end{array}& \begin{array}{c}17=\underset{\phantom{.·}}{40}\\ 11920\end{array}& \begin{array}{c}20=\underset{\phantom{·}}{39}\\ 11716\end{array}& \begin{array}{c}23=\underset{\phantom{.·}}{23}\\ 11493\end{array}& \begin{array}{c}25=\underset{\phantom{.·}}{51}\\ 11269\end{array}& \begin{array}{c}28=\underset{\phantom{.·}}{03}\\ 11051\end{array}& \begin{array}{c}30=\underset{\phantom{.·}}{00}\\ 10845\end{array}& \begin{array}{c}31=\underset{\phantom{.·}}{41}\\ 10656\end{array}& \begin{array}{c}33=\underset{·}{08}\\ 10486\end{array}& \begin{array}{c}34=\underset{\phantom{.·}}{20}\\ 10340\end{array}& \begin{array}{c}35=\underset{\phantom{.·}}{18}\\ 10220\end{array}& \begin{array}{c}36=\underset{\phantom{.·}}{03}\\ 10124\end{array}& \begin{array}{c}36=\underset{\phantom{·}}{35}\\ 10055\end{array}& \begin{array}{c}36=\underset{\phantom{.·}}{54}\\ 10014\end{array}& \begin{array}{c}37=\underset{\phantom{.·}}{00}\\ 10000\end{array}& \\ \phantom{0}& & & & & & & & & & & & & & & & & & & & & \\ 54& & \begin{array}{c}00=\underset{\phantom{·}}{00}\\ 12361\end{array}& \begin{array}{c}\phantom{0}3=\underset{\phantom{·}}{37}\\ 12336\end{array}& \begin{array}{c}\phantom{0}7=\underset{\phantom{·}}{11}\\ 12264\end{array}& \begin{array}{c}10=\underset{\phantom{·}}{39}\\ 12149\end{array}& \begin{array}{c}13=\underset{\phantom{·}}{57}\\ 11998\end{array}& \begin{array}{c}17=\underset{\phantom{.·}}{04}\\ 11918\end{array}& \begin{array}{c}\underset{.·}{19}=\underset{\phantom{·}}{58}\\ 11617\end{array}& \begin{array}{c}22=\underset{\phantom{.·}}{38}\\ 11410\end{array}& \begin{array}{c}25=\underset{\phantom{.·}}{02}\\ 11200\end{array}& \begin{array}{c}27=\underset{\phantom{·.}}{11}\\ 10995\end{array}& \begin{array}{c}29=\underset{\phantom{.·}}{06}\\ 10801\end{array}& \begin{array}{c}30=\underset{\phantom{.·}}{45}\\ 10623\end{array}& \begin{array}{c}32=\underset{\phantom{.·}}{10}\\ 10462\end{array}& \begin{array}{c}33=\underset{\phantom{.·}}{22}\\ 10324\end{array}& \begin{array}{c}34=\underset{\phantom{.·}}{19}\\ 10210\end{array}& \begin{array}{c}35=\underset{\phantom{.·}}{03}\\ 10119\end{array}& \begin{array}{c}35=\underset{\phantom{·}}{35}\\ 10053\end{array}& \begin{array}{c}35=\underset{\phantom{.·}}{54}\\ 10014\end{array}& \begin{array}{c}36=\underset{\phantom{.·}}{00}\\ 10000\end{array}& \\ \phantom{0}& & & & & & & & & & & & & & & & & & & & & \\ 55& & \begin{array}{c}00=\underset{\phantom{·}}{00}\\ 12208\end{array}& \begin{array}{c}\phantom{0}3=\underset{\phantom{·}}{29}\\ 12186\end{array}& \begin{array}{c}\phantom{0}6=\underset{\phantom{·}}{56}\\ 12115\end{array}& \begin{array}{c}10=\underset{\phantom{·}}{16}\\ 12013\end{array}& \begin{array}{c}13=\underset{\phantom{·}}{28}\\ 11872\end{array}& \begin{array}{c}16=\underset{\phantom{.·}}{29}\\ 11707\end{array}& \begin{array}{c}19=\underset{\phantom{·}}{18}\\ 11523\end{array}& \begin{array}{c}21=\underset{\phantom{.·}}{53}\\ 11329\end{array}& \begin{array}{c}24=\underset{\phantom{.·}}{14}\\ 11133\end{array}& \begin{array}{c}26=\underset{\phantom{·.}}{20}:\\ 10941\end{array}& \begin{array}{c}28=\underset{\phantom{.·}}{12}\\ 10758\end{array}& \begin{array}{c}29=\underset{\phantom{.·}}{50}\\ 10591\end{array}& \begin{array}{c}31=\underset{\phantom{.·}}{14}\\ 10438\end{array}& \begin{array}{c}32=\underset{\phantom{.·}}{24}\\ 10308\end{array}& \begin{array}{c}33=\underset{\phantom{.·}}{21}\\ 10200\end{array}& \begin{array}{c}34=\underset{\phantom{.·}}{04}\\ 10113\end{array}& \begin{array}{c}34=\underset{\phantom{·}}{35}\\ 10051\end{array}& \begin{array}{c}34=\underset{\phantom{.·}}{54}\\ 10013\end{array}& \begin{array}{c}35=\underset{\phantom{.·}}{00}\\ 10000\end{array}& \\ & & & & & & & & & & & & & & & & & & & & & \\ & & & & & & & & & & & & & & & & & & & & & \\ \text{Latitude}& & \phantom{0}& \phantom{0}& \phantom{0}& \phantom{0}& \phantom{0}& \phantom{0}& \phantom{0}& \phantom{0}& \phantom{0}& \phantom{0}& \phantom{0}& \phantom{0}& \phantom{0}& \phantom{0}& \phantom{0}& \phantom{0}& \phantom{0}& \phantom{0}& \phantom{0}& \\ \underset{\phantom{.·}}{51}& & \phantom{:}7771:& \phantom{:}7790:& 7847& 7940& 8064& 8214& 8384& 8568& 8761& 8955& 9145& 9326& 9491& 9638& 9765& 9866& 9939& 9984& 10000& \\ \underset{\phantom{.·}}{52}& & 7880& 7898& 7952& 7139& 8156& 8298& 8460& 8635& 8818& 9003& 9184& 9355& 9514& 9655& 9775& 9872& 9942& 9985& 10000& \\ \underset{\phantom{.·}}{53}& & 7986& 8003& 8054& 8136& 8247& 8381& 8535& 8701& 8874& 9049& 9221& 9384& 9536& 9671& 9785& 9877& 9945& 9986& 10000& \\ \underset{\phantom{.·}}{54}& & 8090& 8105& 8154& 8231& 8336& 8462& 8607& 8765& 8929& 9095& 9258& 9413& 9558& 9686& 9795& 9883& 9947& \underset{.·}{9987}& 10000& \\ \underset{\phantom{.·}}{55}& & \phantom{:}8191:& 8252& 8252& 8324& 8423& 8542& 8678& 8827& 8982& 9140& 9295& 9442& 9580& 9701& 9805& 9888& 9949& 9987& 10000& \\ \begin{array}{c}\phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}\\ \phantom{0}\end{array}& & \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \phantom{\text{\_\_\_\_\_\_\_\_\_\_\_}}& \end{array}\\ \hline\end{array}$

The use of this Table to finde the Sun or Stars Altitude uppon Every 5^th Azimuth: for y^e Latitude of $51:52:53:54:55$ Against the Lat' under the Degrees of Every 5^th Azimuth to ${90}^{\mathrm{degrs}}$: you will finde two sumes the first or uppormost sums Sheweth the degrees & min of the the {sic} Equinoctiall Altitude uppon that Azimuth the Next sums under which Being multiplyed with the :S'ine: of the declination: cutt of foore figuers to the Right hand from y^e product: then the degree & minute of the sine of the Remainer Being Added to y^e degree & min of the Equinoctiall Altitude sheweth the degree & min of y^e Altitude uppon that Azimuth for North declination: But if you Substract it from the Equinoctiall Altitude the degree & Min of the Remaner will shew y^e Altitude for y^t Azimuth for Sou^th Declinatio{.} Example Lat' 53: the declination ${23}^{\mathrm{degs}}={31}^{\min }$ Eather North or South: I demaund the Sunn or Stars Altitude or depression uppon the 60: Azimuth Eather Northwards or Southwards from the East or west: I finde the summ for y^e Azimuth under the 60: Azimuth Against ${53}^{\mathrm{degs}}$ of y^e Lat' to bee :10486: w^ch sum I Multiply by the Sine of ${23}^{\mathrm{degs}}={31}^{\min }$ w^ch is $\begin{array}{rr}& 16486\\ & \underset{\_}{\phantom{0}3990}\\ & 943740\\ & 94374\phantom{00}\\ & \underset{\_}{\phantom{0}31458\phantom{000}}\\ \text{facit —}& \mathrm{4183/9140}\end{array}$ Rest Nearest 4184: whole sine is ${24}^{\mathrm{degs}}={44}^{\min }$ which being Added to y^e Equinoctiall w^ch is $\begin{array}{cc}& {33}^{\mathrm{deg}}=\underset{.·}{08}\mathrm{\prime }\\ & {24}^{\phantom{\mathrm{deg}}}=44\phantom{\mathrm{\prime }}\\ \text{facit —}& {57}^{\phantom{\mathrm{deg}}}=\underset{.·}{52}\mathrm{\prime }\end{array}$ w^ch ${57}^{\mathrm{degs}}={52}^{\min }$ sheweth the Altituded uppon the 60^th Azimuth Southwards of the East or west for north declination{.} But for South declination the depression uppon the 60^th Azimuth Northwards of y^e East or West will be ${57}^{\mathrm{degs}}={\underset{.·}{52}}^{\min }${.}
But if I Add Substract my said sum w^ch is $\begin{array}{cc}& {33}^{\mathrm{d}}=08\\ & {24}^{\phantom{\mathrm{d}}}=44\\ \text{Rest —}& {08}^{\phantom{\mathrm{d}}}=24\end{array}$ Being the Suns Altitude uppon y^e 60: Azimuth Southwards of the East or West for South declination: w^ch is his depression uppon y^t Azimuth for North declination Northwards &c, I Demaund the Altitude of Hercus & Lyra uppon the Afforesaid 60^th &|A|zimuth & Lat' $\begin{array}{rr}{\text{y}}^{\text{e}}\text{su}\stackrel{\_}{\text{m}}\text{is —}& 10486\\ \text{the declination of' hercus being}{45}^{\mathrm{degs}}={38}^{\min }\text{the sine theareof is}7149{\text{w}}^{\text{ch}}\text{su}\stackrel{\_}{\text{m}}\text{being Multiplyed thus —}& \underset{\_}{\phantom{0}7149}\\ \text{facit —}& \mathrm{7496/4414}\end{array}$ Rest 7496: the su^m theareof is — ${48}^{\mathrm{degs}}={\underset{.·}{34}}^{\min }$ $\begin{array}{ll}{\text{w}}^{\text{ch}}\text{being Added to}& 33=\underset{.·}{08}\\ & 48=34\\ \text{facit for}{\text{y}}^{\text{e}}\text{Altitude .}& 81=42\mathrm{\prime }\end{array}$ w^ch is Hircus {\is/ {sic}} Altitude uppon y^e 60 Azim South\wards/{.} But if I Substract thus $\begin{array}{cc}& 48\mathrm{`}=34\mathrm{\prime }\\ & {33}^{\phantom{\mathrm{`}}}=08\\ \text{Rest —}& 15\phantom{\mathrm{`}}=26\end{array}$ Being the Altitude of Hircus uppon y<sup>e</sup> 60<sup>th</sup> Azimuth North Wards
I demaund the Altitude of Lyra uppon the said 60<sup>th</sup> Azimuth the sum is 10486 w<sup>ch</sup> Summ I multiply by the sine of Lyras declination w<sup>ch</sup> is — $38=30$ $\begin{array}{rr}{\text{y}}^{\text{e}}\text{sine of'}{\text{w}}^{\text{ch}}\text{is —}& \underset{\_}{\phantom{00}6225}\\ \text{facit —}& \mathrm{6527/5350}\end{array}$ Rest 6527 $\begin{array}{ll}\hfill \text{being}{\text{y}}^{\text{e}}\text{sine of'}& {40}^{\mathrm{degs}}={45}^{\min }\\ & {33}^{\phantom{\mathrm{degs}}}=08\\ \hfill \text{facit —}& {73}^{\phantom{\mathrm{degs}}}=53:\end{array}$ y<sup>e</sup> Altitude Being uppon y<sup>t</sup> Azim Southwards of y<sup>e</sup> East or West: But if you substract $\begin{array}{cc}\text{from}& 40\mathrm{`}=45\mathrm{\prime }\\ \text{—}& {33}^{\phantom{\mathrm{`}}}=08\\ \text{Rest —}& 07\phantom{\mathrm{`}}=37\end{array}$ for y^e Altitude Northwards of y^e East or West {so} upon y^t Az{.} The Like is to be Observed for y^e Sunn or any Other Star for Every 5^th or 10^th Azimuth Or by proportion to any degree of the Azimuth Or any point of y^e Compass If y^t you make proportion of boath summs: vizd y^t Sum of the Azimuth &: Likewise the degrees & minutes of the Equinoctiall Altitude &c{.}

The Next is the Altitude of y^e Sunn or Starr uppon any |5^th| Azimuth to finde the declination{.}

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For the Resolveing of this Question w^ch is of Excelent use for the findeing of the Suns place in y^e Ecliptick Or his Longitude or the day of the Month Or the declination of any fixed star or the Lat' or declination of any plannet &c this Question being one of the three principall termes whearby is Resolved Moast of the Moast usuall problemes in Astronimy therefore I have at the bottom of the Aforesaid table under Every 5^th or 10^th Azimuth to ${90}^{\mathrm{degrs}}$ of Azimuth Given the proportionable summs whearby is found the Sunn or Stars declination{.} Example Lat' 53: I find the suns Altitude uppon y^e 60^th Azimu\th/ to be ${57}^{\mathrm{degs}}={52}^{\min }$ Being southwards of the East or west I demand the declination $\begin{array}{ll}\hfill \text{the Altitud being}& {57}^{\mathrm{degs}}={52}^{\min }\\ \hfill \text{the Altitude of}{\text{y}}^{\text{e}}\text{Equinoctiall uppon the}{\text{60}}^{\text{th}}\text{Azimuth Southwards}{\text{w}}^{\text{ch}}\text{I substact is —}& {33}^{\phantom{\mathrm{degs}}}=08\\ \hfill \text{Rest —}& {24}^{\phantom{\mathrm{degs}}}=44\end{array}$ w^ch ${24}^{\mathrm{degs}}={44}^{\min }$ I finde the sine theareof to be 4184 w^ch sum I sett doune then I Looke at y^e bottome of the table under y^e 60^th Azimuth aganst y^e Latitude I finde the sum 9536 w^ch sum I Multiply by 4184: w^ch multiplyed by 9536: facit 3989/8624: Rest Nearest 3990: w^ch is the sine of ${23}^{\mathrm{degs}}={31}^{\min }$ the Declination desired{.} Againe the Altitude of Hircus uppon the Afforesaid \60^th/ Azimuth being ${81}^{\mathrm{degs}}={42}^{\min }$ Southwards form {sic} y^e East or west I demand the declination: the Equinoctiall Azimuth uppon y^t \60^th/ Azimuth is ${33}^{\mathrm{degs}}={08}^{\min }$ w^ch I substract from ${81}^{\mathrm{degs}}={42}^{\min }$ Rest ${48}^{\mathrm{degs}}={34}^{\min }$ the Sine thereof is $7497·$ w^ch being Multiplyed with the Sum of y^e Azimuth w^ch is 9536: facit 7149/1392: Rest 7149: w^ch is the Sine of ${45}^{\mathrm{degs}}={38}^{\min }$ the declination desired:

To Calculate the Afforesaid Tables for the finding the Sun or Stars Altitude uppon any Azimuth: Or there Altitude uppon any Azimuth to find the declination{.} First for y^e Equinoctiall Altitude uppon any Azim\uth/ Multiply the Tangent of the Complement of the Latitude Given By the sine of y^e Azimuth Given cutt of foare figuers to y^e Right hand: then the Tangent of y^e Remainer sheweth y^e Altitude uppon y^t Azimuth{.} Thus haveing found the Equinoctiall Altitude uppon the Azimuth Given: The Next is to finde the Second found Sum w^ch Summs ar sett at the bottome of the Table for y^e most Redyest g way of finding the Declination when the Altitude & Azimuth is Given: Which is thus found: Multiply the Secant of the Equinoctiall Altitude of y^t Azimuth Given by the sine of the Lat' Cutt of foare figuers to the Right hand from the product Then the Remainer is the Second found Summ: Example y^e Equinoctiall Altitude uppon the 60^th Azimuth in y^e Lat' 53 is ${33}^{\mathrm{deg}}={\underset{.·}{08}}^{\min }$ the Secant thereof is — 11942: Which summ I Multiply by y^e Sine of ${53}^{\mathrm{degs}}=00$: w^ch is $\begin{array}{rr}& 11942\\ & \underset{\_}{\phantom{0}7986}\\ \text{facit —}& \mathrm{9536/8812}\end{array}$: Facit: Rest 9536: w^ch is the Sum desired: Now the Altitude of the Sunn or any of the Said Stars might as well be found uppon y^e said 60 Azimuth as well by this Sum 9536: as well as by the Said Summ shewed befoare w^ch weare 10486: Onley this perfomes {sic} the work by Multiplication but y^e Sum 9536 performes it by Division{.} Example y^e declin^t ${23}^{\mathrm{dr}}={31}^{\mathrm{m}}$ y^e Sine I multiply p 10000 $\begin{array}{rrr}\text{thus —}& 39900000& \left(\begin{array}{cc}\text{Quotient}& \\ 4183& \text{nearest}\hfill \end{array}\right.\hfill \\ \text{the Divisor is —}& \hfill 9536\hfill \end{array}$ w^ch sheweth y^e Sine of ${24}^{\mathrm{degrees}}={44}^{\min }$ as beffore w^ch Add & Substracted as before the worke is the same as shewed befoare for y^e Suns declinat. But if y^t you would have the said sum 10486: & so performe the worke by Multiplication as shewed by the former Exampls Multiply the Radius by y^e Radius w^ch is heare 10000 $\begin{array}{rrr}\text{thus —}& 100000000& \left(\begin{array}{cc}\text{Quotient}& \\ 10486& \text{: —}{\text{w}}^{\text{ch}}\text{is the Afforesaid Summ defined \&c.}\hfill \end{array}\right.\hfill \\ \text{the divisor is —}& \hfill 9536\hfill \end{array}$

thus have I shewed 2 wayes for y^e finding of y^e Altitude of the Sunn or any Star upon Any Azimuth & y^t by a duble way of working so y^t the product of one Multiplication as shewed beffore will shew the A{illeg}|lt|itude uppon the Azimuth Lett it be Eather South East or South West Nor East or Norwest the declination being Eather North or Sou\th/ /&c\