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 ye Coronation And To ye Speaker of the commons 518 Medals for the members & Officers' {illeg} of that house To {illeg} the Mr of ye 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 ye house of Commons: in all 563. I desire that the numbers to be delivered to ye Coffers & that for for forreign ministers upone each account may be settled by a signe manual, & that a minute maby be made for allowing 4li 9s pr ounce for f the Gold & 3s 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 sijusvis ca{illeg} Si chorda arcus cujus a ab ejusdem sagitta {illeg}producta secetur &

Proposita In Curvis omnibus Si chorda 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 punctoū contractus & commune habent centrum curvaturæ ibi in easdem partes incurvantur, commune habentes centrum curvaturæ.

Lemm. XII.

Proposita quacun linea curva, si chorda & sagitata cujusvis arcus ejus hujus Curvæ ducantur & 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 variar{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 estse potuit motus et mutationis & omnis & [amnis rerum diversitatis quæ in mundo accursit] mutationis ac diversitatis rerum, ideo Deum veteres Deum ἀ{illeg}υτοκίνητον dixerunt.

Αὐτοκίνητοςν et Deus Agens Principium primum, quod de fato et Natura dici notn 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 estse debet, ideo 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 infiniti 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, æququali motu angulari propterea quod in directum semper jacent et

Generare dicitus fili{illeg}uoss in sui similitudine quando vivere facit & intelligere Creavit hominem quando formavit ex terra & generavit in filium sibi similem quando vivere fetcit Gen 21.27 & 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 $\mathrm{p}\mathrm{q}=\mathrm{ALB}=\frac{{\overline{)2\mathrm{SIL}}}^{\mathrm{q}}}{4{\mathrm{SI}}^{\mathrm{q}}}=\frac{{\mathrm{HI}}^{\mathrm{q}\mathrm{q}}}{4{\mathrm{SI}}^{\mathrm{q}}}={\mathrm{IL}}^{\mathrm{q}}$.