# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/806933011:0359 # Permalink to this reading: https://leibnizlegible.com/page/806933011:0359?run=74 # Title: Lexicon Technicum: Or, An Universal English Dictionary Of Arts And Sciences (shelfmarks Leibn. Marg. 71; ZEN Leibn. Marg. 71) # Folio - , page id 806933011:0359 # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=806933011&page=359 # Source image: https://digitale-sammlungen.gwlb.de/content/806933011/jpgs/default/00000359.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 122 lines, status machine # Lines: 122 recognised, mean confidence 0.87 # Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. # Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text. # Wording rule: say "the machine reads it as …", never "Leibniz wrote". # After the first blank line: the recognised lines in reading order, one per line. 4. Fo Suberact a Mixt Number from a WBole Number. First, Subtract etie Fractional pare trom Vnier, borroned From che whole Number siven, and. ser doin che Remainder; thien addins chie Integer borro d, 10 ihe Integers oF che Mlixt Number, Suberaet the Caid Sum trom che Whole Numiber; and co che Remainder annex che Fractional Part first Found, andris done. This 3 = From 9, Jcares 5 = 5. To. Subtract a Fraction from a Mixt Number. r. IF che Fraction siven, be lels thanthe Fracti- onal part oF che Mixt Number, ony Subtract che Fraction From the Fractional parr, and annex che Remainders io the Inteser parr oF the MixI, and ris done. Thus : Trom 63, leaves 62. 2. Dur irhen etie Fraction given, is greater chan the Fractional parc oF the Mixc Number: Subiract che Fraction From Vnier, and add che Remainder co che Fractional pare oP che NIXE Number; ehen lessenine che Inceeral parr ot the Mixc Number by Onicy, aunex che Fractional Pare (las Foune) co ic. Thus Trom 6 3 leares 55. C ASF. 6. To Suberact one Mixt Number from another. Fractions; but It cher De Compound Fractions, re duce cheri ro simple ones, anid procced as in he Wrhen the Inregral parr, and Fractional part ot Rest Rule. ehie Mixc Number to be Subtracted, are borh leNCr chan the Incegers and Fractional pares of the ocher Mixe Number; onty subtract che lesser Trireger From the greater, and the lesser Fraction From the greater, and to che Remainder ot the Inregers, an nex che Remainder ot che Fraction, and risdone. Thus 2 =2 From 5 , 2 leares 3 13OF 3 5 C A S F When the Fractional parr oF the Mixr Numibet (c0 be Subtracted) is sreacer chan the Fractiona ParE OF ThC OTheF MIXE NunIiber: First, Suberact che sreacer Praction From Vniey atid add the Remainder ro che Fractional parr ol cheocher MixtNumber; wvhich Sum, 25 che Fr2 ctional pare of ihe Remainder Coustuc, is r0 bc KeDE. Etien add Oniry co che lesser Intepral pare, ane Subrract ihe Sum From the greater Inresral part and eo che Remainders anner the Fractional par betore reserved, and eis done. ThuS, 2 2 from 7 3, rests 4 33. Mulsiplication os Vulear Eractions. Fractions, only Mulriply ehie Numerators one by anocher for a new Numerator, and che Denomina EOFS FOF Q HCW DenOinaTOE. Thus, L inco s produces:;. be reduced to an Improper Fraction, ard chen PrO ceed as in the last Rule. Thus, 5 inco 3: Bires sin and = inco 11 = 40. dolucion et ille Contonnuum in ihe hacd or Bony eectutee au iu a Malracouo tcaltem under che Tonoue, Which beins exrended ro0 FaF coardche Tip of cheTonsue, hinders Children in Suckins, Whence e) ae lald to be Longue. rr d. pu, e is cied co rhe lover parr ol che Glans OF C Penh. N. B. In Mulciplication of Fractions, Etie Pro duet is lels in Value chan cicher Mulciplicanc et Mulciplicarot. Oecacre i aliMulciplicari ons, as Oniey is torhie Mulciplicaror, lo is chie ulciplicand torhie Produet; or 25 s Is lo cither Factor, (0 is che ochet Lalt 10 hC eroduet. Bur Oniiy is bigper chan cirstet La. lbr (it ihe Fractions ale Proper) and chere- Product. Thus in Whole Numbers, TE 5 be miulriplied by 3: 40. Wrheretore in Fract oS ale, abl: 7 : 8 : 32 3 OF251 : 3 ::: 72 Buc LIs Gleater chian cicher = OF 3. WHeretore tbre etchet et Mle h De Elearer chan che o cwil BC, ad 1: 5.. 0. 40, 61, 2. 6. cirtex Ot CHCHL ITus D BSSCFCan 3 = Odision in Fractions. 1. Irhen the Fractions proxolca ale voMM lingle; MIIIIPI) The DenOminaTOF Ot lHC Dirisor by EC Numerator ot the Diridend; ene Product is the Numerator oF ehC OMOrC. Then Mulriply ehe Numeraror or cn Dirilor. by che Denommator ot che Dividend, ihie Product is che: Denominaror ot rhe Onoclent. THuS, 3) 3 (33 2. IF cicher Diridend, Do, e bo De Wrtiole or Nixt Numbers; reduce chemro improxer N. B. That in Division os Fractions, the Ouo- cenr is alvars grearer chanche Mdend; Be- caule in all livition, asthe Divilor isto Vni- Cs, l0is che Diridend eo rtie Ouorient; a5 H diride 12, tvilt DC 253 : 1 : - 12. 4. Nou 3 is preater ctian L, WMelCtere F2 must in tohere ; lo elohan i; vohrereso1 be biseer chan 4. Bur in Fractions, 25 3: Y ust allo be lelo Mhan 33. FRACTORA Osis, the breaking ot a MIC, l Paers of che Body FR ENOMI, is thac Ligamene wtrereby rhe Pre- FRAISES, in Fonisicarion, ae pointed Scaties Exed in Bulwarkes made ot Farrh, on the onc side OF chic Rampare a licele belo etic Paraper. These Scakes beins From 7 t0 B Foor lons, are driven in almost half Wvay inco che Rarrt, and prelent chekt Aero prevene Scalades and Lelerrion. LRAME, is che Our- WorkoF a Clock OF W acch, consistins ot che Plares and Pillars, and which con cains in ic che WVheels and che rest ot che Work. FRANCHIISE, in Law, iscaten to be 2 Priri. lege or Eixemprion trom ordinary furildiction, and Merimes an immunies trom Tribure: Ie is cicher Perlonal ox Real; chac is, belongine t0 a Person immeciaets, oc exlebys Mequs ps lio ee lac vtace. Poines somewhac soaxins coward theField. They, .Wten he Fractions propoled are boch sinele 2. Et OHEDC L NIXEOK BHOLC LMIIIBer, it mus