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 which is that he hath tryed my Numbers & found them hold well: which hath Incoradged me once moore to present him with another Burd, of the same fether hatched at the 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 which moast of them ar by duble wayes of working which I had Allmost filled a Book with which: which I thought once that 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 that 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 vaine: I suppoase I shall not Receve an answer of which while I be in London for about Saterday or Munday next at the furthest I thinck that I shall take shipp & so fall doune to Graves End which perhapes if an answer Come soone I may Receive it there otherwayes it may be by affter ships: Haveing no moore at present 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 October the 1^st 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 the Latitude of $51:52:53:54:55$ Against the Latitude 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 & minute of the Equinoctiall Altitude uppon that Azimuth the Next sums under which Being multiplyed with the :Sine: of the declination: cutt of foore figuers to the Right hand from the product: then the degree & minute of the sine of the Remainer Being Added to the degree & minute of the Equinoctiall Altitude sheweth the degree & minute of the Altitude uppon that Azimuth for North declination: But if you Substract it from the Equinoctiall Altitude the degree & Minute of the Remaner will shew the Altitude for that Azimuth for South Declination{.} Example Latitude 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 the Azimuth under the 60: Azimuth Against ${53}^{\mathrm{degs}}$ of the Latitude to bee :10486: which sum I Multiply by the Sine of ${23}^{\mathrm{degs}}={31}^{\min }$ which 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 the Equinoctiall which is $\begin{array}{cc}& {33}^{\mathrm{deg}}=\underset{.·}{08}\mathrm{\prime }\\ & {24}^{\phantom{\mathrm{deg}}}=44\phantom{\mathrm{\prime }}\\ \text{facit —}& {57}^{\phantom{\mathrm{deg}}}=\underset{.·}{52}\mathrm{\prime }\end{array}$ which ${57}^{\mathrm{degs}}={52}^{\min }$ 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 the East or West will be ${57}^{\mathrm{degs}}={\underset{.·}{52}}^{\min }${.}
But if I Substract my said sum which 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 the 60: Azimuth Southwards of the East or West for South declination: which is his depression uppon that Azimuth for North declination Northwards &c, I Demaund the Altitude of Hercus & Lyra uppon the Afforesaid 60^th Azimuth & Latitude $\begin{array}{rr}{\text{y}}^{\text{e}}\text{su}\stackrel{\_}{\text{m}}\text{is —}& 10486\\ \text{the declination of' hercus being}{45}^{\mathrm{degs}}={38}^{\min }\text{the sine theareof is}7149{\text{w}}^{\text{ch}}\text{su}\stackrel{\_}{\text{m}}\text{being Multiplyed thus —}& \underset{\_}{\phantom{0}7149}\\ \text{facit —}& \mathrm{7496/4414}\end{array}$ Rest 7496: the summ theareof is — ${48}^{\mathrm{degs}}={\underset{.·}{34}}^{\min }$ $\begin{array}{ll}{\text{w}}^{\text{ch}}\text{being Added to}& 33=\underset{.·}{08}\\ & 48=34\\ \text{facit for}{\text{y}}^{\text{e}}\text{Altitude .}& 81=42\mathrm{\prime }\end{array}$ which is Hircus {his} Altitude uppon the 60 Azimuth Southwards{.} 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 the 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 which Summ I multiply by the sine of Lyras declination which 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 $\begin{array}{ll}\hfill \text{being}{\text{y}}^{\text{e}}\text{sine of'}& {40}^{\mathrm{degs}}={45}^{\min }\\ & {33}^{\phantom{\mathrm{degs}}}=08\\ \hfill \text{facit —}& {73}^{\phantom{\mathrm{degs}}}=53:\end{array}$ the Altitude Being uppon that Azimuth Southwards of the 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 the Altitude Northwards of the East or West {so} upon that Azimuth{.} The Like is to be Observed for the 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 the Compass If that you make proportion of boath summs: vizd that Sum of the Azimuth &: Likewise the degrees & minutes of the Equinoctiall Altitude &c{.}

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

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For the Resolveing of this Question which is of Excelent use for the findeing of the Suns place in the Ecliptick Or his Longitude or the day of the Month Or the declination of any fixed star or the Latitude 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 Latitude 53: I find the suns Altitude uppon the 60^th Azimuth to be ${57}^{\mathrm{degs}}={52}^{\min }$ Being southwards of the East or west I demand the declination $\begin{array}{ll}\hfill \text{the Altitud being}& {57}^{\mathrm{degs}}={52}^{\min }\\ \hfill \text{the Altitude of}{\text{y}}^{\text{e}}\text{Equinoctiall uppon the}{\text{60}}^{\text{th}}\text{Azimuth Southwards}{\text{w}}^{\text{ch}}\text{I substact is —}& {33}^{\phantom{\mathrm{degs}}}=08\\ \hfill \text{Rest —}& {24}^{\phantom{\mathrm{degs}}}=44\end{array}$ which ${24}^{\mathrm{degs}}={44}^{\min }$ I finde the sine theareof to be 4184 which summ I sett doune then I Looke at the bottome of the table under the 60^th Azimuth aganst the Latitude I finde the summ 9536 which summ I Multiply by 4184: which multiplyed by 9536: facit 3989/8624: Rest Nearest 3990: which 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 for the East or west I demand the declination: the Equinoctiall Azimuth uppon that 60^th Azimuth is ${33}^{\mathrm{degs}}={08}^{\min }$ which I substract from ${81}^{\mathrm{degs}}={42}^{\min }$ Rest ${48}^{\mathrm{degs}}={34}^{\min }$ the Sine thereof is $7497·$ which being Multiplyed with the Sum of the Azimuth which is 9536: facit 7149/1392: Rest 7149: which 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 the Equinoctiall Altitude uppon any Azimuth Multiply the Tangent of the Complement of the Latitude Given By the sine of the Azimuth Given cutt of foare figuers to the Right hand: then the Tangent of the Remainer sheweth the Altitude uppon that Azimuth{.} Thus haveing found the Equinoctiall Altitude uppon the Azimuth Given: The Next is to finde the Second found Sum which Summs ar sett at the bottome of the Table for the most Redyest way of finding the Declination when the Altitude & Azimuth is Given: Which is thus found: Multiply the Secant of the Equinoctiall Altitude of that Azimuth Given by the sine of the Latitude Cutt of foare figuers to the Right hand from the product Then the Remainer is the Second found Summ: Example the Equinoctiall Altitude uppon the 60^th Azimuth in the Latitude 53 is ${33}^{\mathrm{deg}}={\underset{.·}{08}}^{\min }$ the Secant thereof is — 11942: Which summ I Multiply by the Sine of ${53}^{\mathrm{degs}}=00$: which is $\begin{array}{rr}& 11942\\ & \underset{\_}{\phantom{0}7986}\\ \text{facit —}& \mathrm{9536/8812}\end{array}$: Facit: Rest 9536: which is the Sum desired: Now the Altitude of the Sunn or any of the Said Stars might as well be found uppon the said 60 Azimuth as well by this Summ 9536: as well as by the Said Summ shewed befoare which weare 10486: Onley this performes the work by Multiplication but the Summ 9536 performes it by Division{.} Example the declination ${23}^{\mathrm{dr}}={31}^{\mathrm{m}}$ the Sine I multiply per 10000 $\begin{array}{rrr}\text{thus —}& 39900000& \left(\begin{array}{cc}\text{Quotient}& \\ 4183& \text{nearest}\hfill \end{array}\right.\hfill \\ \text{the Divisor is —}& \hfill 9536\hfill \end{array}$ which sheweth the Sine of ${24}^{\mathrm{degrees}}={44}^{\min }$ as beffore which Add & Substracted as before the worke is the same as shewed befoare for the Suns declination. But if that you would have the said sum 10486: & so performe the worke by Multiplication as shewed by the former Exampls Multiply the Radius by the Radius which 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 the finding of the Altitude of the Sunn or any Star upon Any Azimuth & that by a duble way of working so that the product of one Multiplication as shewed beffore will shew the Altitude uppon the Azimuth Lett it be Eather South East or South West Nor East or Norwest the declination being Eather North or South &c