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 there be no decrease

I Delivered to my Lord Bradford 300 Medals of gold, for the Coronation And To the Speaker of the commons 518 Medals for the members & Officers' of that house 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 the house of Commons: in all 563. I desire that the numbers to be delivered upon each account may be settled by a signe manual, & that a minute may be made for allowing 4^li 9^s per ounce for 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 $\overline{\mathrm{Pu}+\mathrm{uV}}=\mathrm{VPv}$ – – – – – et PV (ex natura sectionum conicarum) æqualis erit $\frac{2{\mathrm{DC}}^{\mathrm{q}}}{\mathrm{PC}}$.

Adde uPv untrinque et habebitur quadratum chordæ arcus PQ prodibit æquale rectangulo VPv

Proposita In Curvis omnibus Si cho{rda} arcus segmentis sagittæ æquetur rectangulo sub segmentis chordæ & interea arcus minuatur & evanescat: Circulus qui transit per terminos sagittæ & arcum evanescentem tangit e Curvam tanget concentrice.

Curvas se mutuo tangere concentrice dico quæ sunt ejusdem curvaturæ ad punctum contractus ibique in easdem partes incurvantur, commune habentes centrum curvaturæ.

Lemm. XII.

Proposita quacunque linea curva, si chorda & sagitta cujusvis arcus hujus Curvæ ducantur et sagitta producta chordam secet & eousque 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 ad punctum contactus in easdem partes incurvantur, idque æqualiter, commune habentes centrum curvaturæ. Circulus autem qui transit per terminos chordæ et terminum alterutrum sagittæ , transibit per terminum alterum sagittæ per Prop XXXV Lib III Elem. 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 diversitate locorum ac temporum diversa est rerum Natura, et diversitas illa non ex necessitate metaphysica, quæ utique eadem est semper et ubique sed ex voluntate sola entis necessario existentis oriri potuit. Sola voluntas principium fons et origo esse mutationis ac diversitatis rerum, ideoque Deum veteres ἀυτοκίνητον dixerunt.

Αὐτοκίνητον et Agens primum, quod de fato et Natura dici non potest. Pro diversitate locorum ac temporum diversa est rerum finitarum natura, et diversitas illa non ex necessitate metaphysica, quæ utique eadem est semper et ubique, sed ex voluntate sola Entis intelligentis et necessario existentis oriri potuit. Et hæc de Deo, de quo &c

Agens primum ut sit primum, ἀυτοκίνητον esse debet et propterea potestate volendi præditum est: quod de Fato et Natura dici non potest. Pro diversitate locorum ac temporum diversa est rerum omnium finitarum natura, et diversitas illa non ex necessitate Metaphysica (quæ utique eadem est semper et ubique) sed ex voluntate sola Entis intelligentis et necessario existentis oriri potuit, . Et hæc de Deo de quo utique ex phænomenis 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, æquuali motu angulari propterea quod in directum semper jacent et

Generare dicitus filios in sui similitudine quando vivere facit & intelligere Creavit hominem quando formavit ex terra & generavit in filium sibi similem quando vivere fecit Gen 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 $\frac{{\mathrm{LB}}^{\frac{1}{2}}-{\mathrm{LA}}^{\frac{3}{2}}}{\sqrt{\mathrm{LA},\mathrm{LB}}}$. $\mathrm{LI}=\frac{{\mathrm{AS}}^2}{2\mathrm{SI}}$

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

$\frac{1}{{\mathrm{x}}^3}$. $-\frac{1}{2\mathrm{x}\mathrm{x}}$. $\frac{1}{2{\mathrm{LA}}^2}-\frac{1}{2{\mathrm{LB}}^2}$. ${\mathrm{x}}^{-\frac{3}{2}}$. $\frac{2}{{\mathrm{x}}^{\frac{1}{2}}}$. $\frac{{\mathrm{SA}}^{\mathrm{q}}}{\mathrm{SI}}=\mathrm{PS}$. $\frac{{\mathrm{SA}}^{\mathrm{q}}-{\mathrm{SI}}^{\mathrm{q}}}{\mathrm{SI}}=\mathrm{PI}$. $\frac{{\mathrm{SA}}^{\mathrm{q}}+{\mathrm{SI}}^{\mathrm{q}}}{2\mathrm{SI}}=\mathrm{LS}$ $\frac{{\mathrm{SA}}^{\mathrm{q}}+{\mathrm{SI}}^{\mathrm{q}}\pm {}^2\mathrm{ASI}}{2\mathrm{SI}}=\underset{\mathrm{LA}}{\mathrm{LB}}$. $\frac{{\mathrm{BI}}^{\mathrm{q}}}{2\mathrm{SI}}=\mathrm{LB}$. $\frac{{\mathrm{AI}}^{\mathrm{q}}}{2\mathrm{SI}}=\mathrm{LA}$. $\sqrt{\frac{8{\mathrm{SI}}^{\mathrm{c}}}{{\mathrm{AI}}^{\mathrm{c}}}}-\sqrt{\frac{8{\mathrm{SI}}^{\mathrm{c}}}{{\mathrm{BI}}^{\mathrm{c}}}}=\sqrt{8{\mathrm{SI}}^{\mathrm{c}}}$ 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 $\sqrt{8{\mathrm{s}}^3}\times \frac{{\mathrm{w}}^3-{\mathrm{w}}^3}{{\mathrm{v}}^3{\mathrm{w}}^3}$, 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 $\frac{3\mathrm{r}\mathrm{r}+\mathrm{s}\mathrm{s}}{{\mathrm{t}}^3\sqrt{2\mathrm{s}}}=\frac{\mathrm{s},\mathrm{ALB}\text{ in }3\mathrm{r}\mathrm{r}+\mathrm{s}\mathrm{s}}{6{\mathrm{t}}^3\phantom{\mathrm{ALB}\text{ in }3\mathrm{r}\mathrm{r}}}=\frac{{\mathrm{s}}^3+3\mathrm{r}\mathrm{r}\mathrm{s}}{6{\mathrm{t}}^3}\mathrm{ALB}$ $\mathrm{ALB}={\mathrm{LS}}^{\mathrm{q}}-{\mathrm{SA}}^{\mathrm{q}}={\mathrm{LI}}^{\mathrm{q}}+2{\mathrm{LI}}^{\mathrm{q}}+{\mathrm{SI}}^{\mathrm{q}}-{\mathrm{AS}}^{\mathrm{q}}$. 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 ${\mathrm{w}}^3-{\mathrm{v}}^3$ $=\frac{1}{6}\mathrm{s}\times \frac{{\mathrm{w}}^3-{\mathrm{v}}^3}{\mathrm{v}\mathrm{w}}=\frac{1}{6}\mathrm{s}$ 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 $\mathrm{p}\mathrm{q}=\mathrm{ALB}=\frac{{\overline{)2\mathrm{SIL}}}^{\mathrm{q}}}{4{\mathrm{SI}}^{\mathrm{q}}}=\frac{{\mathrm{HI}}^{\mathrm{q}\mathrm{q}}}{4{\mathrm{SI}}^{\mathrm{q}}}={\mathrm{IL}}^{\mathrm{q}}$.