The present state of the coinage in relation to the fineness of the moneys

The present state of the Coynage in relation to the fineness of the moneys.

Assaying & refining are operations of the same kind. The Assayer refines a small piece of any mass of gold or silver & by the decrease of its weight makes his report: & if the {sic} be no decrease of its weight makes his

I Delivered to my Lord Bradford 300 Medals of gold, for y^e Coronation And To y^e Speaker of the commons 518 \Medals/ for the members \& Officers'/ {illeg} of that house To {illeg} \the M^r of y^e {Cer.} weightier/ |And| 40 Medals \more were made/ for forreign ministers. These \last/ were weightier then the rest, & may now contein an ounce of gold in each Medal. There are now 45 members more in y^e house of Commons: in all 563. I desire that the numbers to be delivered to y^e Coffers & that for for forreign ministers \upone each account/ may be settled \by a signe manual/, & that a minute mab|y| be made for allowing 4^li 9^s p^r ounce for {f} the Gold & 3^s a piece for the wast & workmanship upon bringing in a Bill.

${\mathrm{Qv}}^{\mathrm{q}}=\frac{\mathrm{PvG},{\mathrm{DC}}^{\mathrm{q}}}{{\mathrm{PC}}^{\mathrm{q}}}=\mathrm{PvG},\frac{\mathrm{uV}}{\mathrm{vG}}=\mathrm{Pv},\mathrm{uV}.$ ${\mathrm{PQ}}^{\mathrm{q}}={\mathrm{Qv}}^{\mathrm{q}}+{\mathrm{Pv}}^{\mathrm{q}}+\mathrm{Pv},\mathrm{uV}={\mathrm{Pv}}^{\mathrm{q}}+2\mathrm{Pv},\mathrm{uV}=\mathrm{Pv},\mathrm{Pv}+2\mathrm{uV}$./ ${\mathrm{Qv}}^{\mathrm{q}}=\mathrm{Pv},\mathrm{uV}$. ${\mathrm{QP}}^{\mathrm{q}}={\mathrm{Qv}}^{\mathrm{q}}+{\mathrm{Pv}}^{\mathrm{q}}+\mathrm{uvP}=\mathrm{Pv},\mathrm{uV}+{\mathrm{Pv}}^{\mathrm{q}}+\mathrm{uvP}=\mathrm{Pv},\mathrm{uV}+\mathrm{Pv}+\mathrm{uv}=\mathrm{Pv},\mathrm{PV}$

Adde uPv et habebitur ${\mathrm{QP}}^{\mathrm{q}}[=\mathrm{Pu},\mathrm{uV}+\mathrm{Pu},\mathrm{Pv}=\mathrm{Pu},\mathrm{PV}]=\mathrm{Pv}$ in uV $\overline{\mathrm{Pu}+\mathrm{uV}}=\mathrm{VPv}$ – – – – – et PV (ex natura sectionum conicarum) ejusdem æqualis erit $\frac{2{\mathrm{DC}}^{\mathrm{q}}}{\mathrm{PC}}$.

Adde uPv untrin et habebitur QP quad æquale quadratum chordæ arcus PQ prodibit æquale rectangulo VPv

Circulus curvam contingit concentrice

\In Curvis omnibus lineæ {sijus}vis ca{illeg}/ Si chorda arcus cuj{us} a \ab ejusdem/ sagitta {illeg}|pr|oducta secetur &

\Proposita/ In Curvis omnibus Si cho{rda} arcus segmentis sagittæ æquetur rectangulo chor sub segmentis chordæ & interea chorda \arcus/ minuatur & evanescat: Circulus qui a{illeg} qu{illeg} arcum {a} evanescentem tangit & transit per terminos sagittæ ejusdem erit curvaturæ Cum {eruit} Curva in puncto contactus {illeg} \& arcum evanescentem tangit e/ Curvam tanget concentrice.

Curvas se mutuo tangere concentrice dico quæ sunt ejusdem curvaturæ {illeg}|ad| puncto|ū| contractus & commune habent centrum curvaturæ \ibi/ in easdem partes incurvantur, commune habentes centrum curvaturæ.

Lemm. XII.

Proposita quacun linea curva, si chorda \& sagita|t|a/ cujusvis arcus ejus \hujus Curvæ/ \duca\n/tur/ & ejusdem arcus sagitta \quævis/ producta se mutuo se cent et sagitta producta chordam secet & eous producatur ut rectangulum sub segmentis sagittæ æquale sit rectangulo sub segmentis chordæ, et \arcus ille/ interea minuatur in infinitum et evanescat: circulus qui semper transit per terminos chordæ et sagittæ, tanget arcum evanescentem concentrice.

Curvas se mutuo tangere concentrice dico, quæ sunt eji{illeg} {illeg} ad punctum contactus æqualiter et in easdem partes æqualiter incurvantur, \id æqualiter,/ commune habentes centrum curvaturæ. Circulus autem qui transit per terminos chordæ et terminum alterutrum \alterutrum/ sagittæ \in curva situm/, transibit per terminum alterum sagittæ per Prop XXXV Lib III Elem. Et curva quæ transit per terminos sagittæ & chordæ et t{illeg} ac transeundo per tria Curvæ puncta eandem obtinebit curvaturam ubi puncta illa coeunt.

$\begin{array}{r}2304\phantom{0}\\ 288\phantom{0}\\ -\phantom{0}\mathrm{28,8}\\ \overline{2553.4}\\ 4.9\\ -\phantom{.}9\\ \overline{25557.4}\end{array}$

$\begin{array}{r}2304.12.6\\ 288\phantom{.1}9.\phantom{0}\\ 3\phantom{.1}1.\phantom{0}\end{array}$

$\begin{array}{rr}\begin{array}{r}2304.13.\phantom{1}6\phantom{⁤\frac{1}{4}}\\ 3.\phantom{13.11⁤\frac{1}{4}}\\ 288.\phantom{1}9.\phantom{1}2⁤\frac{1}{4}\\ \underline{-28.16.11\phantom{⁤\frac{1}{4}}}\\ 5.\phantom{1}9⁤\frac{1}{4}\end{array}& \begin{array}{r}2596.02.\phantom{1}8⁤\frac{1}{4}\\ -28.16.11\phantom{⁤\frac{1}{4}}\\ \overline{2567.\phantom{1}5\phantom{.1}9⁤\frac{1}{4}}\end{array}\end{array}$

Pro varietate \diversitate/ locorum ac temporum varia{r}{illeg}{r} \diversa est/ rerum Natura, et diversitas illa non ex necessitate metaphysica, quæ uti eadem est semper et ubi non sed aliunde quam ex voluntate \sola/ entis necessario existentis oriri potuit. Sola voluntas principium fons et origo est|s||e| \potuit/ motus et mutationis \&/ omnis & [amnis \rerum/ diversitatis quæ in mundo accursit] mutationis ac diversitatis rerum, ideo \Deum/ veteres Deum ἀ{illeg}|υ|τοκίνητον dixerunt.

Αὐτοκίνητο{ς}|ν| et Deus \Agens Principium primum/, quod de fato et Natura dici not|n| potest. et ex voluntate sola Entis necessario existentis Pro diversitate locorum ac temporum diversa est rerum \fini{illeg}tarum/ natura, et diversitas illa non ex necessitate metaphysica, quæ uti eadem est semper et ubi, sed ex voluntate sola Entis intelligentis et necessario existentis oriri potuit. Et hæc de Deo, de quo &c

Agens primum \ut sit primum,/ ἀυτοκίνητον est|s|e debet, ide\o/ inter facultate \esse debet et propterea potestate/ volendi præditum est \est:/ quode de Fato et Natura dici non potest. Pro diversitate locorum ac temporū diversa est rerum \omnium/ finitarum natura, et diversitas illa non ex necessitate Metaphysica (quæ uti eadem est semper et ubi) sed ex volutate {sic} sola Entis intelligentis et necessario existentis oriri potuit, \voluntas antea et h{illeg}{} /{entis} infinit{i}\ voluntas dominium inducit summum inducit./. Et hæc de Deo de quo uti ex phæmenis {sic} disputare, ad Philosophiam experimentalem pertinet.

Apud Ægyptios symbolum Dei erat serpens per mundum extensus.

Deus creat omnia componendo, generat intelligentes vivificando

|{illeg}dist| circum terminum suum communem, æquq|u|ali motu angulari propterea quod in directum semper jacent et

Generare dicitus fili{illeg}u|os|s in sui similitudine quando vivere facit & intelligere Creavit hominem \quando formavit/ ex terra & generavit in filium sibi similem quando vivere fet|c|it Gen 2|1|.27 & 2.7. Cal. 1. 15, 18. Rev. 1.5

$\mathrm{ALB}={\mathrm{LI}}^{\mathrm{q}}-{\mathrm{AS}}^{\mathrm{q}}$. $\frac{{\mathrm{SI}}^2\times \overline{{\mathrm{LS}}^2-{\mathrm{AS}}^2}}{3\sqrt{2\mathrm{SI}}\times \sqrt{{\mathrm{LA}}^3}}-\frac{{\mathrm{SI}}^2\times {\mathrm{LS}}^2-{\mathrm{AS}}^2}{3\sqrt{2\mathrm{SI}}\times \sqrt{{\mathrm{LB}}^3}}=\frac{{\mathrm{SI}}^{\mathrm{q}}}{3\sqrt{\mathrm{SI}}}$ in $\frac{{\mathrm{LS}}^2-{\mathrm{AS}}^2\times {\mathrm{LB}}^{\frac{3}{2}}-{\mathrm{LA}}^{\frac{3}{2}}}{{\mathrm{LA}}^{\frac{3}{2}}\times {\mathrm{LB}}^{\frac{3}{2}}}$ $\frac{{\mathrm{SI}}^{\frac{3}{2}}}{3\sqrt{2}}$ in $\frac{\mathrm{LB}}{{\mathrm{LA}}^{\frac{1}{2}}}-\frac{\mathrm{LA}}{{\mathrm{LB}}^{\frac{1}{2}}}$ seu in $\frac{{\mathrm{LB}}^{\frac{1}{2}}-{\mathrm{LA}}^{\frac{3}{2}}}{\sqrt{\mathrm{LA},\mathrm{LB}}}$. $\mathrm{LI}=\frac{{\mathrm{AS}}^2}{2\mathrm{SI}}$

$\frac{6{\mathrm{SI}}^{\mathrm{q}},\mathrm{SL}-6{\mathrm{SI}}^{\mathrm{q}},\mathrm{SI}-4{\mathrm{SI}}^3}{3\mathrm{SI}\phantom{-6{\mathrm{SI}}^{\mathrm{q}},\mathrm{SI}-4{\mathrm{SI}}^3}}=\frac{6{\mathrm{SI}}^{\mathrm{q}},\mathrm{LI}-4{\mathrm{SI}}^3}{3\mathrm{LI}}$

$\frac{1}{{\mathrm{x}}^3}$. $-\frac{1}{2}\mathrm{x}\mathrm{x}$$-\frac{1}{2\mathrm{x}\mathrm{x}}$. $\frac{1}{2{\mathrm{LA}}^2}-\frac{1}{2{\mathrm{LB}}^2}$. ${\mathrm{x}}^{-\frac{3}{2}}$. $\frac{2}{{\mathrm{x}}^{\frac{1}{2}}}$. $\frac{{\mathrm{SA}}^{\mathrm{q}}}{\mathrm{SI}}=\mathrm{PS}$. $\frac{{\mathrm{SA}}^{\mathrm{q}}-{\mathrm{SI}}^{\mathrm{q}}}{\mathrm{SI}}=\mathrm{PI}$. $\frac{{\mathrm{SA}}^{\mathrm{q}}+{\mathrm{SI}}^{\mathrm{q}}}{2\mathrm{SI}}=\mathrm{LS}$ $\frac{{\mathrm{SA}}^{\mathrm{q}}+{\mathrm{SI}}^{\mathrm{q}}\pm {}^2\mathrm{ASI}}{2\mathrm{SI}}=\underset{\mathrm{LA}}{\mathrm{LB}}${illeg}. $\frac{{\mathrm{BI}}^{\mathrm{q}}}{2\mathrm{SI}}=\mathrm{LB}$. $\frac{{\mathrm{AI}}^{\mathrm{q}}}{2\mathrm{SI}}=\mathrm{LA}$. $\sqrt{\frac{8{\mathrm{SI}}^{\mathrm{c}}}{{\mathrm{AI}}^{\mathrm{c}}}}-\sqrt{\frac{8{\mathrm{SI}}^{\mathrm{c}}}{{\mathrm{BI}}^{\mathrm{c}}}}=\sqrt{8{\mathrm{SI}}^{\mathrm{c}}}$ in $\frac{{\mathrm{BI}}^{\mathrm{c}}-{\mathrm{AI}}^{\mathrm{c}}}{{\mathrm{AI}}^{\mathrm{c}}{\mathrm{BI}}^{\mathrm{c}}}$ $\frac{{\mathrm{SA}}^{\mathrm{q}}-{\mathrm{SI}}^{\mathrm{q}}}{2\mathrm{SI}}=\mathrm{LI}$. $\begin{array}{lll}\pm {\mathrm{AS}}^3& +3{\mathrm{AS}}^2,\mathrm{SI}\pm 3\mathrm{AS},{\mathrm{SI}}^2& +{{\mathrm{SI}}^2}^{}\\ & +3& +\end{array}$. $\frac{{\mathrm{BI}}^{\mathrm{c}}-{\mathrm{AI}}^3}{{\mathrm{AI}}^{\mathrm{c}},{\mathrm{BI}}^{\mathrm{c}}}=\frac{6{\mathrm{AS}}^{\mathrm{q}}+{}^2\mathrm{SI}^{\mathrm{q}}\text{ in }\mathrm{SI}.}{{\mathrm{HI}}^6}$. ${\mathrm{HI}}^6={\mathrm{AS}}^6-3{\mathrm{AS}}^4{\mathrm{SI}}^2+3{\mathrm{AS}}^2{\mathrm{SI}}^4-{\mathrm{SI}}^6=8{\mathrm{LI}}^3{\mathrm{SI}}^{\mathrm{c}}$. $\frac{{\mathrm{SI}}^{\mathrm{q}},\mathrm{ALB}}{3\sqrt{2\mathrm{SI}}}\times \sqrt{8{\mathrm{SI}}^{\mathrm{c}}}$ in $\frac{6{\mathrm{AS}}^{\mathrm{q}}+{}^2\mathrm{SI}^{\mathrm{q}}\times \mathrm{SI}}{8{\mathrm{LI}}^{\mathrm{c}},{\mathrm{SI}}^{\mathrm{c}}}$ ${\mathrm{SI}}^{\mathrm{c}}\times \frac{{\mathrm{AS}}^{\mathrm{q}}+2{\mathrm{SI}}^{\mathrm{q}}}{2{\mathrm{LI}}^{\mathrm{c}},{\mathrm{SI}}^{\mathrm{c}}}\times \mathrm{SI}$. $\frac{\mathrm{SI},\mathrm{ALB}}{2{\mathrm{LI}}^{\mathrm{c}}}\times {\mathrm{AS}}^{\mathrm{q}}+\frac{1}{3}{\mathrm{IS}}^{\mathrm{q}}=\frac{\mathrm{SI},{\mathrm{LS}}^{\mathrm{q}}-\mathrm{SI},{\mathrm{SA}}^{\mathrm{q}}}{2{\mathrm{LI}}^{\mathrm{c}}}\times {\mathrm{AS}}^{\mathrm{q}}+\frac{1}{3}{\mathrm{IS}}^{\mathrm{q}}$ $\frac{3{\mathrm{AS}}^2,\mathrm{SI}}{6\mathrm{LI}}\times \frac{\mathrm{ALB}}{{\mathrm{LI}}^{\mathrm{q}}}+\frac{{\mathrm{SI}}^3}{6\mathrm{SI}}\times \frac{\mathrm{ALB}}{{\mathrm{LI}}^{\mathrm{q}}}$.

$\mathrm{LA}=\mathrm{p}$. $\mathrm{LB}=\mathrm{q}$. $\frac{{\mathrm{q}}^{\frac{2}{3}}-{\mathrm{p}}^{\frac{2}{3}}}{{\mathrm{p}}^{\frac{2}{3}}{\mathrm{q}}^{\frac{2}{3}}}$. $\mathrm{AS}=\mathrm{r}$. $\mathrm{SI}=\mathrm{s}$. $\mathrm{LI}=\mathrm{t}$. $\mathrm{AI}=\mathrm{v}$. $\mathrm{BI}=\mathrm{w}$. ${\mathrm{HI}}^2=2\mathrm{LI}, \mathrm{SI}=2\mathrm{s}\mathrm{t}$.

$\frac{\mathrm{s}\mathrm{s},\mathrm{ALB}}{3\sqrt{2}{\mathrm{s}}^{\frac{1}{2}}}$ in $\frac{1}{{\mathrm{p}}^{\frac{3}{2}}}-\frac{1}{{\mathrm{q}}^{\frac{3}{2}}}$. $\mathrm{p}=\frac{\mathrm{v}\mathrm{v}}{2\mathrm{s}}$. $\mathrm{q}=\frac{\mathrm{w}\mathrm{w}}{2\mathrm{s}}$. $\frac{{\mathrm{s}}^{\frac{3}{2}},\mathrm{ALB}}{3\sqrt{2}}$ in $\frac{{\mathrm{a}}^{\frac{3}{2}}-{\mathrm{p}}^{\frac{3}{2}}}{{\mathrm{p}}^{\frac{3}{2}}{\mathrm{q}}^{\frac{3}{2}}}$ seu in $\frac{\frac{{\mathrm{w}}^3}{2\mathrm{s}\sqrt{2\mathrm{s}}}-\frac{{\mathrm{w}}^3}{2\mathrm{s}\sqrt{2\mathrm{s}}}}{\frac{{\mathrm{v}}^3{\mathrm{w}}^3}{8{\mathrm{s}}^3}}$ seu in $\frac{8{\mathrm{s}}^3{\mathrm{w}}^3-8{\mathrm{s}}^3{\mathrm{v}}^3}{2\mathrm{s}\sqrt{2\mathrm{s}}\times {\mathrm{v}}^3{\mathrm{w}}^3}$ seu in {illeg} $\sqrt{8{\mathrm{s}}^3}\times \frac{{\mathrm{w}}^3-{\mathrm{w}}^3}{{\mathrm{v}}^3{\mathrm{w}}^3}$, seu in $\sqrt{8{\mathrm{s}}^3}\times \frac{6\mathrm{r}\mathrm{r}\mathrm{s}+2{\mathrm{s}}^3}{8{\mathrm{s}}^3{\mathrm{t}}^3}$ ${\mathrm{w}}^3-{\mathrm{v}}^3={\mathrm{r}}^3+3\mathrm{r}\mathrm{r}\mathrm{s}+3\mathrm{r}\mathrm{s}\mathrm{s}+{\mathrm{s}}^3-{\mathrm{r}}^3+3\mathrm{r}\mathrm{r}\mathrm{s}-3\mathrm{r}\mathrm{s}\mathrm{s}+{\mathrm{s}}^3=6\mathrm{r}\mathrm{r}\mathrm{s}+2{\mathrm{s}}^3$. $\frac{\sqrt{2\mathrm{s}}\times \mathrm{s}\mathrm{s}\times \overline{3\mathrm{r}\mathrm{r}+\mathrm{s}\mathrm{s}}}{2{\mathrm{s}}^3{\mathrm{t}}^3}=\frac{\sqrt{2\mathrm{s}}\text{ in }3\mathrm{r}\mathrm{r}+\mathrm{s}\mathrm{s}}{2\mathrm{s}{\mathrm{t}}^3}=\frac{3\mathrm{r}\mathrm{r}+{\mathrm{s}}^3}{{\mathrm{t}}^3\sqrt{2\mathrm{s}}}$. $\frac{{\mathrm{s}}^{\frac{3}{2}},\mathrm{ALB}}{3\sqrt{2}}$ in $\frac{3\mathrm{r}\mathrm{r}+\mathrm{s}\mathrm{s}}{{\mathrm{t}}^3\sqrt{2\mathrm{s}}}=\frac{\mathrm{s},\mathrm{ALB}\text{ in }3\mathrm{r}\mathrm{r}+\mathrm{s}\mathrm{s}}{6{\mathrm{t}}^3\phantom{\mathrm{ALB}\text{ in }3\mathrm{r}\mathrm{r}}}=\frac{{\mathrm{s}}^3+3\mathrm{r}\mathrm{r}\mathrm{s}}{6{\mathrm{t}}^3}\mathrm{ALB}$ $\mathrm{ALB}={\mathrm{LS}}^{\mathrm{q}}-{\mathrm{SA}}^{\mathrm{q}}={\mathrm{LI}}^{\mathrm{q}}+2{\mathrm{LI}}^{\mathrm{q}}+{\mathrm{SI}}^{\mathrm{q}}-{\mathrm{AS}}^{\mathrm{q}}${illeg}. 3

$\frac{{\mathrm{s}}^{\frac{3}{2}},\mathrm{p}\mathrm{q}}{3\sqrt{2}}$in $\frac{{\mathrm{q}}^{\frac{3}{2}}-{\mathrm{p}}^{\frac{3}{2}}}{\mathrm{p}\mathrm{q}\sqrt{\mathrm{p}\mathrm{q}}}=\frac{{\mathrm{s}}^{\frac{3}{2}}}{3\sqrt{2\mathrm{p}\mathrm{q}}}$ in ${\mathrm{q}}^{\frac{3}{2}}-{\mathrm{p}}^{\frac{3}{2}}=\frac{{\mathrm{s}}^{\frac{3}{2}}\times 2\mathrm{s}}{3\sqrt{2}\times \mathrm{v}\mathrm{w}}\times \frac{{\mathrm{w}}^3}{2\mathrm{s}\sqrt{2\mathrm{s}}}-\frac{{\mathrm{v}}^3}{2\mathrm{s}\sqrt{2\mathrm{s}}}=\frac{\mathrm{s}}{6\mathrm{v}\mathrm{w}}$ in ${\mathrm{w}}^3-{\mathrm{v}}^3$ seu in $=\frac{1}{6}\mathrm{s}\times \frac{{\mathrm{w}}^3-{\mathrm{v}}^3}{\mathrm{v}\mathrm{w}}=\frac{1}{6}\mathrm{s}$ in $\frac{6\mathrm{r}\mathrm{r}\mathrm{s}+2{\mathrm{s}}^3}{2\mathrm{s}\mathrm{t}}=\frac{3\mathrm{r}\mathrm{r}\mathrm{s}}{6\mathrm{t}}+\frac{{\mathrm{s}}^3}{6\mathrm{t}}$/ scribendo $2\mathrm{s}\mathrm{t}$ pro $\mathrm{p}\mathrm{q}=\mathrm{ALB}=\frac{{\overline{)2\mathrm{SIL}}}^{\mathrm{q}}}{4{\mathrm{SI}}^{\mathrm{q}}}=\frac{{\mathrm{HI}}^{\mathrm{q}\mathrm{q}}}{4{\mathrm{SI}}^{\mathrm{q}}}={\mathrm{IL}}^{\mathrm{q}}$.