An Account of a Controversy Betwixt Stephano de Angelis, Professor of the Mathematicks inPadua, and Joh. Baptista Riccioli Jesuite as It Was Communicated Out of Their Lately PrintedBooks, by That Learned Mathematician Mr. Jacob Gregory, a Fellow of the R. SocietyAuthor(s): Jacob GregorySource: Philosophical Transactions (1665-1678), Vol. 3 (1668), pp. 693-698Published by: The Royal SocietyStable URL: http://www.jstor.org/stable/101276 .

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(693)

Monday, J,tone i 5. i 66o.

The Contelnts. An Ac c ount of a Contre'verf betwiixt S teplhano de Angelis, and

John Baptiala Riccioli, concerning the Motion of the Eartki. An Enlargement of the Obfervations formerly pubtliJli't Numb. 27. ipredby a CuriousTravello#r to jamac

' WhT7ere dio ot

c.urr JDxfccu;fcs ato#t the Steams of the Sea; the Colour of the Sea - 'various Plants and Animals in jamaica, and othcr i/lands of the Caribes ; the qualities of Tobacco growirg,e, in N iti-ou Ground; Hlurricans5 a wayto make aBIoat ride at Anchor inth)e main Led4; the elfFelis of the Changre ofClimateon Human Bodies; ,a probable way of Preventing and Curingr Sick nefs in Tra'vel- lors to the Weft-Indies, &c. An ExtraC7 of a Printed Letter, addrtjfled to the Publithier, touching a late direrence, rifen at Pa - ris, about the Transfufion of Bloud. An Account of two Rooks%* I. THE PROGRESS aind AD)VANCEMENr

ofKNOWLEDGE fince the dayes of ARISTOTLE; by JOS. GLANVILL. Jr. ABRAH. COULEIL Sex Li-~ bril PLANTARUM.

An Account of a Controveofy betwixt S tephiano d e Angel is, Profejfor of thje

Matbematicks inPadua, and Job. Bipt`ta Ricc'oli eu' ~sit was communicated ouit of their- lately Printcd Rooks, by

that Learned xMahematicia4n Mr. Jacob Gregory, a Fellow, of the R. Society.

rIcioli i'n his Almagejium Novam pr-etends to have found out feveral new demnonftrative Arguments agailnfi t -e Motion

of the Earth. Steph. de Angelis, conceivingz his Argruments ro Ggg be 1

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(694) be none of the ftrongeft, taketh occafion to let the world fee, that they are not more efteem'd in It,y,tlhan in o. her placesoMan- fredi, in behalf of Riccioli, endeavours to anfwer the Objeftions of Anneli, and this latter replyes ro Manfrcdi's Anfwer. The fubflxance of their difcourfe is this following.

Altlhough the Arguments of Riccioli be many, yet the ftrencgt o1 tlelne confins cllieflyin thefe three:

Thle fri.

Mtultha copora gravia, dimiffa per Aerem, in Plano eAqlIatorf exi/entem, defcenderent ad Terrain curn Velocitatis Incremento reali & notabili, & non tinturm apparenti. Sed fi tellus moveretur motu ditrrn,o tanti m circa Jui centrtum, nmila corrpo ra avia, dimia per Aerem, in Plano . quatoris exi ientem, defcendcrent ad Terramn cur,m clocitatis incremento rcali ac notabil, Cfd tanturm cuim appa- renti. E, Te// ou t non mov,ctur, Ylut non movePtur dimrno tant'Rnm mo ot .

1 hle Jcond.,

Si Tellms moveretlr mot/u diurno, an,t ctilzm aroma, muIto debi- lior cefct ilus clobi bombardici explofi in Septentrioncm out Meri dienm,quamn ab occidente in orientcm, At conjqfetcns eJ falf, m. E. & antecedens.

The thi d.

Si Terh/ls diursn rcvol/tione owvwrctur, Globes argilltacc tn ciarumn 8. rx altituddine Romanorum pedutm 240. per aerem qriitum dimiffgis) obliq/o deJccnii in Ter ram dclberetur abque incremexto reall ac phy ico vel.citatis, vel certe nun quaim t,azto, quanta ei roprortiof P cr yI cis ac foni per cafirm ex dita altitudine fa.;. Sedp faeriiss ft ahbfrdum. E. &( prius.

In Anfwepr to tlefirf of thicfe Arguments, Aageli deniCeth tle Jirnor,-whicch RiAcciol prcte;and to- plove thus 5

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( 6p ) Si 7Tellus movtretur Jol diurno motn, aiquad G4rve, dimif lf

ex Trrts vertice C ii Plaeo.4qt#atoris erifentis, defcriberitfau mottx naturali portionem linex CTI, que effet ad omnem fenfum circ/laris.

, Fig. I.

This Angeli denies, fhewing by Computation, that Riccioli his Obfei vation proveth no fuch thing. For (faith Angeli) accord- ing to Riccioli, in one fecond of an hour the weiglit defcends 15 ; foot; in 2 feconds, 60 foot; in 3 feconds 135 tooti and fo continually the fpaces from the beginning are in duplicate pro- portion of the Time from the beginning and, according to the

Gggg 2 fame

A .2·

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(69) fame Author; AB (the femi-diameter of the Earth ) is of 2 5870000 foot, and BC (the height of the Tower of the Afi- neill in Bononia) of 240 foot i and therefore AC is 25870240, whlicll ath the fame proportion to PS, 15 foot, to wit, ye fall in one fecond, which AC in parts 2000COOOCo hath to FS

1159 24 1896 ; but fuppofing,with Riccili, CSIA a femi-circle,

FS is 53 patts, of which AC is I ooooooc ooo: Hence conclu- deth' ngeli, that CSIA is no wayes near to a femi-circle; which is moft lure, iffo be the weight fall not to the Center of the Earth precifely in 6 hours: For ,in this cafe of Riccioli, the weight falls to the Center of the Earth in 21 minmtes and 53 feconds.

alanfredi in his Anfwer for Riccioli affirms, that Angeli underftands not the Rule of Three, in giving out FS. tor 11596 54356 of which AC is 2oooooocooo000: And /Ingei 2596 24189

'

in his Reply affimnls his Analogy to be fo clear, that there can be nothing laid mo-e evident than it felf to confirm it i referring in the mean time the further determination to Geometeis.

Angeli might have anfwer'd Riccioli's Argument, granting the weight to move equally in a femi-circle, by diftinguifhing hi:s Minor thus;

Nht'/a Corpora gravia defcendercnt ad Terrain ctur velocitati ·ic:rcmento reali ac rotabili, fi Velocitas computetur in circum- fei cntia femi- circuli; Minorpropofitio ect vera. At non computatur ita Motu4 dcfcenfivws: nam hic motus ,qualis in circumfcrenti jemi- circuli CIA. componitur ex motua equali in uadrante CD, & motu accleSratl in fimidiametro mohili CA; & hi motus ac- ecra,tus in f cmidialmrtro efl verus & Jimapkex motus defcerifivns

in qua acrcepf ioe lMinorpropoftio c(l f alfifSima, &e Riccioli etiam expericntnis contraria. But it feems, that Angeli anfivereth other- wife, to make Ficcicli fenfible, that CIA is no femicircle ; con- cerning the nature of which Line they debate very much through- out the twhole difcourfe.

The fecod A: gument is much infifled upon by Angeli,to make i's iLoI u tn clear to vulgar capacities; but the fubftance of all is rThan the Canon-ball hath not only that violent motion,imprefled i-y the iire, but alfo all thefe motions proper to the Earth, which

;'t-e ommunicated to it by the impulfe received fItom the Earth: f0:'y

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('67) for, the Ball, going from Weft to Eaf, hath indeed two impulf's, one from the Earth, and another from the Fire but this impulfe from the Earth is alfo common to the mark, and therefore the Ball hits the mark only with that fimple impulfe, received from the Fire, as it doth being fhot towards the North or South; as, Angeli doeth excellently illuftrate by familiar examples of Motion.

To Riccioli his thirdArgument A4ngeli anfwereth, defiring him to prove the fequel of his Major, which Riccioli doeth,fuppofing the curve, in which the heavy body defcends, to be compofed of many finall right lines; and proving, that the motion is almoft always equal in thefe lines; and after fome debate, concerning the equality of motion in thefe right lines, Angeli anfvers, tlhat the equality of motion is not fufficient to prove the equality of percuf'ion and found, but that there is necefTary alfo equal angles ofintidexce which in this cafe he proveth to be very unequal. To illultrate this more, let us prove)that,other things being alike,the proportion of two percuffions is compofed of the direa propol tion of their velocities, and of the diret proportions of the Sines of their angles of incidence. Supponamw anteam fequens principium, nempf quodpercufsiones (cateris paribt, ) fint in direcfa prr/por- tioe cunm veocitatibus, qiibus mobile .ppropinqfat planum rcfi/ ens Fig. zda. Sit planmm CF, fintque duo mobili' omri modoe qualia, & fimilia, qua motu qutali accedant ai Pun/o A. ad planum CF, in retis AD, AF: dico,percufsionem inpunao ) adpercufionem in punilo F. effe in ratione compOfita ex ratione 'veocitatis in recia AD, ad velocitatem in AF, & ex ratione fins anguli ADE ad finum 4ngaliAFE. Ex pncSo A in planum CF, fit recla AE normalis, fitque reWa AC quvalis re/ch AF, e& AB aqualis reet? AD, &- planum BGH, parallelur plane CF: ulpponamis mobile, priorilus fimile aqu ale, moeri equaliter in refta AC, eadem velocitate, qua mvetur mobile in rela A D: quoniam plana BGH, C F int parallela, & motus in reffa AC elt tqualis, igitur mobile' eadem 'z- loritate acedit adplanum BlI, qua ad planum C F, & proirded pfer cufiiones in plsnil; B, C, afnt xqales B atque perycufio in pitnF D, ef adpercufionem in punao B, ut re/a AE ad re /ffam A , feHt (eb ,quales re(Ca AD, AB) t fin; anguli ADE ad fiirm akgtul ABH, quod fic plobo w'Ivlocita mobilis in reda Ar), efi quaqt :

re!-e.

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(6os) velocitati miis in regfa AB, ipfi AD ]equai, C ide eodcm ten. pore per fiitur utraq te re/a AD, AB; &" proinde eodem ten ore perfcitnltur accefsiones adplanaref/lgentia AE, AH; ideoque velo- citates accefsionum adplana reffitentiafunt in direc7a ratione AE ad AHl, a!qeide percfjsio in punSto D. ej adpercufsionem in pun£to C. in eadem ratione AE adAH ; nempe ut Sinus anguli incidentix ADE. ad finum anguli incidentix ACE, vel AFE. ouoniam ,vitem recrJ AC, AF, ,equaliter inclinant adplanum CF, mobilia in rezeis AC,.AF, accedunt adplanum CF, in eadem proportione qua moventur in rec7is AC) AF; C5 ideo percufsio in C e/F ad percufsionem in F in ratione velocitatis motus in ACJfef in AD ad velocitatem motus in. AF; At demonflratum ee ante, percufsionem in punato D adpercufsionem in puns o C, ejfe in rationefinus an- gali ADEadfnum anguli AFE, & nunc demonfJratum elf, per- cufsionem in puncao C cffe adperctfsionem in punSlo F, t velocitas motus in AD ad velocitatem motus in AF. Igitur ex 5.defin 6. Ele- rmentorum, ptrcufs io in D, ep adpercufsionem in F,in ratione compa- fita ex ratione finus anguli incidentie ADE, ad finum anguli inci- dentik A FE, & ex ratione velocitatis in AD advelocitatem in AF; quod demonftrare oportuit. Neminem moveat, quod hxc demon- /ftrtio adftrisa fit motibus aqualibus in lineis rettis & planis re- fiftentibus 5 eft enim vera in omni cafu : nam, cumpercufsiones fiant in pAuno, in hoc coincidunt rectum, curvum, tquale, & inxquale; fi autem in pun7ispercufsiones non fiant, de ilfis non potet dari con- Jideratio geometrica, fedjudicandus el conclufoinis defeltus fecun- dum defeaum materie ar conditionibus requifitis, ficut femper fieri debet, dum demon irationes geometrica corpori phyfico appliF cantor.

In Angeli his reply to Ufanfreddi, he maketh mention of an Experiment, which (as was related to him by a Svediph Gentle- man) had been made with all due circumfpec6ion by Cartefius to prove the Motion of the Earth. The experiment was; He caufed to be ereled a Canon perpendicular to the Horizon; which be- ing 24 times difcharged in that poflure, the Ball did fall 22 times towards the Wef/, and only twice toward the 'aft.

.A/

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