Formula for calculating customs duty, followed by notes on the measurements of Herod's temple and a series of trigonometrical calculations

Author: Isaac Newton

Source: MINT 19/3/444, National Archives, Kew, Richmond, Surrey, UK

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- Revision History
  - 1 January 2001
    - Catalogue information compiled by Rob Iliffe, Peter Spargo & John Young
  - 29 September 2011
    - Catalogue exported to teiHeader by Michael Hawkins
  - 21 May 2017
    - Transcribed by Will Scott
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<444r>

Question

To find the net duty upon East-India goods by 12 Ann {C}

Answer

Let D be the duty p^r cent \upon 100^li/ by former Acts \of P/ & say, a|A|s \the value/, 100^li + D to D the net duty D so is is {sic} 1 to N. And the number N being once found the Question will be thus {illeg}|an|swered. From the value by the candle subduct the allowances by for prompt payment & warehouse room {illeg} & the remainder multiplied by N will be the net duty desired

Proof

For let the Remainder by R. {sic} And \& NR will be the duty p^r cent upon R − NR, \the remainder of that duty{.}/ For/ as the value 100^li + D is to the net duty D in any one case\in {illeg}/, so is 1 to {illeg}|N|, & so is the value R to the net duty NR in any other case. For The value R the remainder R is {illeg} the value upon w^ch the net duty is to be {illeg}|pa|id & this value is to the net duty upon it in a given proportion & this p{illeg}|r|oportion is that of 100^li + D to D or 1 to N.

The Iews who first set down \wrote\published// \in writing the Talmud/ the measures of Herods Temple, omitted some measures \{then}/ {illeg}|o|n either side of y^e altar & only set down the summ of \{w^ch}/ the cubits & the writers who followed \made y^e {measures} following Iewish/ |omitted| |cubits| /& the following Iewish writers\ dividing tha|e|t summ equally \of the cubits omitted into two equal parts/ placed the altar nearer to y^e south side of the court then to y^e north side: whereas they should have divided thes|at|e cubits\summ/ unequally so that y^e altar might have stood in y^e center of the court.

<444v>

in 2 $\frac{1}{4}$ it runs 13_∟8×13_∟8 × 4 dig = 76176 dig. In 1' it runs 338_∟56 dig.

In 24''' it falls 32 dig & moves 64^dig

In 1'' it moves 160 dig

In {illeg} it moves 9600 {illeg}|d|ig.

In 135'' = 2 $\frac{1}{4}$ it /runs\ 16_∟12 × 16_∟12 × 4 {illeg} \× 13_∟8/ dig in length = 14344 dig.

In 1' it moves 6{illeg}|3|75_∟09461