**This** **table** **of** **Vlacq'****s** **was** **published**, **with** **an** **English** **explanation** **prefixed**, **at** **London** **in** 1631 **under** **the** **title** **Logarithmicall** **Arithmctike** ...

**Briggs** **had** **himself** **been** **engaged** **in** **filling** **up** **the** **gap**, **and** **in** **a** **lettex** **to** **John** **Pell**, **written** **after** **the** **publication** **of** **Vlacq'****s** **work**, **and** **dated** **October** 25, 1628, **he** **says**: " **My** **desire** **was** **to** **have** **those** **chiliades** **that** **are** **wantinge** **betwixt** 20 **and** 90 **calculated** **and** **printed**, **and** **I** **had** **done** **them** **all** **almost** **by** **my** **selfe**, **and** **by** **some** **frendes** **whom** **my** **rules** **had** **sufficiently** **informed**, **and** **by** **agreement** **the** **busines** **was** **conveniently** **parted** '**amongst** **us**; **but** **I** **am** **eased** **of** **that** **charge** **and** **care** **by** **one** **Adrian** **Vlacque**, **an** **Hollander**, **who** **hathe** **done** **all** **the** **whole** **hundred** **chiliades** **and** **printed** **them** **in** **Latin**, **Dutche** **and** **Frenche**, **moo** **bookes** **in** **these** 3 **languages**, **and** **hathe** **sould** **them** **almost** **all**.

**Vlacq'****s** **table** **is** **that** **from** **which** **all** **the** **hundreds** **of** **tables** **of** **logarithms** **that** **have** **subsequently** **appeared** **have** **been** **derived**.

**Briggs** **appreciated** **clearly** **the** **advantages** **of** **a** **centesimal** **division** **of** **the** **quadrant**, **and** **by** **dividing** **the** **degree** **into** **hundredth** **parts** **instead** **of** **into** **minutes**, **made** **a** **step** **towards** **a** **reformation** **in** **this** **respect**, **and** **but** **for** **the** **appearance** **of** **Vlacq'****s** **work** **the** **decimal** **division** **of** **the** **degree** **might** **have** **become** **recognized**.

**It** **contains** **seven-figure** **logarithms** **of** **numbers** **from** **I** **to** 100,000, **with** **characteristics** **unseparated** **from** **the** **mantissae**, **and** **was** **formed** **from** **Vlacq'****s** **table** (1628) **by** **leaving** **out** **the** **last** **three** **figures**.

**In** 1794 **Vega** **published** **his** **Thesaurus** **logarithmorum** **completus**, **a** **folio** **volume** **containing** **a** **reprint** **of** **the** **logarithms** **of** **numbers** **from** **Vlacq'****s** **Arithmetica** **logarithmica** **of** 1628, **and** **Trigonometria** **artificialis** **of** 1633.

**Vega** **devoted** **great** **attention** **to** **the** **detection** **and** **correction** **of** **the** **errors** **in** **Vlacq'****s** **work** **of** 1628.

**Babbage** **compared** **his** **table** **with** **the** **Tables** **du** **Cadastre**, **and** **Lefort** **has** **given** **in** **his** **paper** **just** **referred** **to** **most** **important** **lists** **of** **errors** **in** **Vlacq'****s** **and** **Briggs'****s** **logarithms** **of** **numbers** **which** **were** **obtained** **by** **comparing** **the** **manuscript** **tables** **with** **those** **contained** **in** **the** **Arithmetica** **logarithmica** **of** 1624 **and** **of** 1628.