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Full text of "A Summary Account of the General Laws of Motion by Dr. John Wallis, and Dr. Christopher Wren."

(354) 

A Summary Account given by Br. John Wallis, 
of the Genet al Laws of Motion 3 by way of Letter mitten by him 
to the P libit jhr , and communicated to the 11. Society , No- 
vemb # 2<5. 1668. 

PEtis , V. C. ut quae raea func de Motibus arflimandis Principia , paucis 
apcrirevelim- Idautem, fimeminifti, jamolim fadumell, noa mo- 
do in iilo Open, quod ante ofto menfes 11. S-ocietati exhibitum 5 eorum 
juflu prelo fub jedum eft ; fed & jamdudum in duobus fcriptis eidem S$cfo 
uti ante plures Annos exhibkis, quae & Te penes funt :- Quorum alcerum 5 
cxgeneralibusMotusPrincipiis, rationem reddit , qui fieri poflk, ut Ho- 
mo flicu fuo ( Vefiea.n inflando ) faltem Centipondium elevare potis fie 
(quod Experim, ante i&vel i8> annosOvcw^exhibitum , coram Ipfis alU 
quoties fuit repetitum-,) Alterum , varia deExperim # T'<?wa///4wdido t 
phenomena , ex principals Hydroftatiris exponit. 
Summa rei hue. reditu 

r. Si Agens ut A effieir ut E «, Agens ut z A , efficiet ut 2 E • 3 A, tit 
j-E,&c. ceteris paribus : Et, univerfaliter, ^Aut^Ej cu jufcunq; rati* 
onisExponensfit m. 

2.. Ergo, fiVisutVeioveatPondusP; vis«;Vutmovcbit^P f caeter; 
paribus 1 puta, per eandem Longitudinem eodem Tempore, he. ead'em Ce- 

lericate*. 

3. Item, fi Tempore T. moveat illud per Longitudinem L * Tempore 
*T movebit per Longitudinem n L. 

4. Adeoque, fi Vis V, tempore T, moveat PondusP, per Longitudinem 
£• ViswV, Tempore n T, movebit^P, perLongitud. n\. Et prop- 
tcrea, ut VT (faftum ex viribus & tempore) ad PL (faftum expondere 
& Longitudine) fic^wVT, ad m n P L, 

5. Qnoniam Celeritatis gradus funt Longitudinibus eodem Tempore 
jranfadis Proportionates, feu (qu<Kt eodem recidit) reciproce propor- 
tionates Temporibus eidem Longitudini tranfigendse impenfis : ens 

% . C : : ^ • ~G h. e. Gradus Celeritatum inrationecompofita e$ 

Dine&a Longitudinum & Reciproca Tempomm, 

6. Efgo, propter V T. P L :: mnVT.mn? It erit V, -j- : : m V. J *?^|^s 

ft, e, V, PC : : m V.mVC = w P * C = P x w ۥ 

7. Hoeeft, fi VisVmovere pods fit PondusP, CeleritateCr Vis mV 
movebit vel idem Pendus-P, Celer itate m C \ vel eadem Celeritate , Pon- 
dus m P % vel deniqae quodvis Pondus ea Ccleritate 3 ut faftum ex Pondcre 
,& C^^rime fit m P C 

% A*|ue hine dependet omnium Machinarom (pro faclfitandis trotibus) 

conftro? 



sonftruendarum ratio: nempc, utqua ratione augetur Pondus 5 endcmrnl- 

nuatur Celeritas ; quo fiat, ut Faftum ex Celeritate & Pondcre , eadem Vi 

i 
movendo. idem fie : puta V, P C : : V.wPx^C-pC, 

9. Si Pondus P, Vi V, Celericate C, latum , in pondus Qwicfcem (non 
impeditum) m? direfte impingat-, ferentur utraque Celericate ~rr C, 
Nam, propter eandem Vim , ma/ori Ponderi movendo adhibits m , cadem 
ratione minuetur audi Celeritas : nempe V. P C : : V. J - ' m P x — r — - 
C=P"C Adeoque Alterius Impetus (intellige fa ft urn ex J?oiidere 
& Celeritate) fiet j~ PC . Reliqui—^ wPC 

10. Si in Pondus P, (Vi V) Celeritate C latum, direfte impingata- 
Bud, eadem via , majori Celeritate infequens • puta Pondus m? , Ce- 
leritate n C , (adeoque Vi mn V latum ; ferentur ambo Celeritate 

Llb^C. Nam V. PC::w« V.mnVC : : V-f- mn V = *+*'* v. 
1 -j- w * - 

— *j— ' P c = — j*— P * x V — C. Adeoque precedents Impetus 

fiet — t: — P C •, fubfcqjuenti5 y — V— w P C. 

ir. Si Pondera contrariis Viis lata , fibi direfte occurrantfiveimpin- 
gant mutuo , puta , Pondus P (Vi V) Celeritate C, dextrorfum ; & Pon- 
dus m P , . Celeritate * G (adeoque Vi m » V) finiftrorfum : Utriufque Ce- 
leritas, Impetus, Stdireccio, fie colliguntur. Pondus dextrorfum latum, 

reliquo fi quiefceret , inferret Celeritatem •- 1 — C , adeoque Impetum 

~j— m p C , dextrorfum fibique rctineret hanc eandem Celeritatem. 

adeoque Impetum ~jrr^ P C dextrorfum (per Sett. 9,) Pondufque fini- 
ftrorfum latum ( fimili ratione) reliquo fi quiefceret , inferret Celeritatem 
x4-^ C > adeoque Impetum -jS^ PC finittrorfum ; fibique retu 

ncret hanc eandem Celeritatem, adeoque Impetum --', — ;#P C fini- 
ftrorfum. Cum itaque motus utrinque flat ^ Impetus dextrorfum prius !ati ? 

3 7)1 f* 

Jam aggregatus eric ex rr~ PC dextrorfum, & ■ — — PC finiftror- 

fum • adeoque readfe vel dextrorfum vcl finittrorfum , prout illc vel 
hie major fuerit 9 eo impetu qui eft duorum differentia .• h,e. (pofito 
~*P figno dextrorfum , & — liniitrorfum fignificance , ) impetus eric 



I 

2 



( adeoque Dextrorum vel finiftrorfum , prout x vel tnn major fuerit.) 
Et fimiliter Impetus finiftrorfum prius lad , eric + 7^~^FC 

■ — 7 jl. „ m P C " , m P C > Celentas T i C : Adcoque 

dexrrorfum vel finiftrorfum , prout I vel ^ « major fuerit, 

i~> Si vero Pondera nee eademdirede via proced.mc 3 nee dire&econ- 
traria,fed oblique fibi mutuo impinganc • moderandus eritpraecedens Calcu- 
lus pro obliqukatis menfura. Impetus autem oblique impingentis , ad e juf- 
dem Impetum quiefTetfi^Wff^imp'mgeret (caeter. paribus; eft in ea ratio- 
ne qua Radius ad Secantcm anguli Obliqukatis ; ( Quod etiam intelligent 
dum cftjUbiPerpendiculariter, fed Oblique cadit inpercufli fuperficiem 
non minus quam ubi viae mocuum fe mutuo Oblique decuflfant : ) Qua? qui- 
dem Confideracio, cum Calculo priori debite adhibka, determinable 5 
quaenamfutura lint fie Oblique impingentiumCelerkas, Impetus, &dire- 
<ftio , h. e. quolmpecu, qua Celerkate , & in quas partes ab invicem re- 
filient, quae fie impmgunt. Eacfemque eft ratio Gravitationis gravium 
Oblique defcendentiutu,ad eorundem Perpendiculariter defcendentium Gra~ 
vitationum. Quod alibi demonftramus. 

13 Si quae fie impingunt Corpora , intelligantur non abfolute dura 
( prout hadenus fuppofuimus ) fed ita idaii cedentia , ut Elaftica tamen vi 
fe valeant reftituere , bine fieri potent ut a fe mutuo refiliant ea corpora, 
quae fecus effent fimul proceffura ; (& quidem plus minufve , prout haec 
vis reftitutiva major minorve fuerit, ) nempe fi Impetus ex vi reftkutiva fit 
progreffiva major. 

In motibusacceleratis &rctardatis, Impetus pro fingulis momentisisre- 
putandus eft , qui gradui Celeritatis turn acquifito convenk, Ubi autem 
perCurvam fitmotus, eareputanda eft, in fingulis punftis , motus dire- 
<3:io , quae eft Rectae ibidem Tangentis. Et fi quindo motus turn accele- 
ratus vel retardatus fit , turn & perCurvam fiat ( ut in Vibrationibus Pen- 
duli ^ ) Impetus aeftimandus erit , pro fingulis punftis , fecundum turn 
gradum acceleratibnis , turn Obliquitatem ibidem Tangentis. 

Atque hae func (quantum Ego judico) Generates Motuum Leges -, quae 
ad Cafus pmicuiares Calculo func sccommodandce. Quos tamen , fi figil- 
latim perfequi vellem Epiftolae limites tranfilirem ; Neque commode 
fieri poreft fcire <SV£?w^/>7#apparatu,quibus hicabftinendum putavi. Vdc* 
Ox oft. J. 15, Nov smb. 166$, 

Z>r Chrifto- 



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($6 7 ) 

Qr. Chriftopher Wrens 

7htory concerning the fame Subject -, impvted to the R. So- 
ciety Dccemb. 17. la(t , though entertain d by the Author di- 
vers years ago 5 ^#^ ty/7/? d by many Experiments ? made by 
Himfelf and that other excellent Mathematician M. Rook be- 
fore the [aid Society 5 as is attejled by many Worthy Members 
of that Illuftrious Body, 

Lex Naturae de Collifione Corporum. 

Elccitates Corporum prcprU Or maxime Nat males fmt ad Corpora rs~ 
ciproce proportionates, 

Itaque Corpora R. S. habentia prcprias Velocitates , etlam pofi Jm~ 
puff urn retinent proprias. 
ex Na~ Et Corpora R. S. improprias Velocitates habentia ex Impulfu re- 
turn . fiituuntur ai ^/Equilibrium \ hoc efl^ Quantum R fuperat y & 
S deficit a propria Ve lock ate arjc Impulfum, t ant urn ex Impuifu 
abftrahitm ab R & additur ipfiS & c contra. 
jQuare Coltifio Corporum proprias Velocitates habendum dquipollet Librg 
cfcillcnti faper Centrum Gmvitath, 

Et Colli fi® Corporum improprias Velocitates habendum tquipoltet Libra fa • 
per bind Centra aquatiter tonic inde h Centre Gravitatis diflantia : Libra ve- 
ro Jugum , ubiopus ejl^producitur, 

Itaque Corporum ctqua/ium improp»ie moventium t res fmt cafpu. Corporum 
vere inaqnalium improprU moventium {five ad contr arias five ad eafdem 
partes ) decern funt omnino Cafes , quorum quinque oriuntur ex Conver- 
fiene, 



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N-ttnra obfervat regd ts Additionis & Subduttienis Speciofar. 

An Account of two Boohs. 

I. HISTORIA CjELESTIS-, Ex Libris & Com- 
mentariis M.Stis. Obfervationum Vicennalium T Y- 
CHONIS BRAHE 5 Dani , Auguftse Vindelic. 
yf». 1666, in Folio. 

THefe Obfervations of the Noble 7)wk , as they were pro. 
cured and preferv'd by thofe Three Mighty Emperours , 
RUDOLPH. II. FERDINAND. II. and III-, fo 
they were lately by the Command of his Imperial Majefty L E- 
OPOLD made publick. They are ufaer'J in by a Liber Pre- 
bgomems, compendioufly reprefenting the Obfervations made 
from the time of the very Infancy of Aftronomy unto that of 
its Refhuration by the Illuftrious Tycho^ and reduced into 7. 
Gaffe s, viz. 

1. The Babylonian Obfervations j from A. before Chrift 721. 

unto A. 43 a. 

2. The Grecian ; from A. before Chrift 432. onto th: be- 
ginning of the Vulgar Chriftian Account.. 

3. The Alexandrian-, from A. Cbrifti r. until A. 827. 

4. rheSyro-Perfan; from A. C. 827. unto 1457. 

5. The Norimbergian 5 from ^.C.T457» unto 15 op, 

& The