New-York tribune., 1876-06-03
LOCAL MISCELLANY.
"rEcIPRocAL IDENTITY"
.usrAyts FRANKENsTEfN's LECTURE - HIS M"
MATHEMATICAL PRINCIPLE.

tUsTAyUs FRANKENS1EiH'S LhCICh" - NO 49,
MATHEMATICAL PRINCIPLE.
| Gustavus Frankenstein lectured yesterday
,,oaooc ar stinway Han on Reciprocal Identity ana
r. ,.o,0r,cols a New Principle in Mathematcs
e. ATTENDANCE of gentlemen small but several nun
Il ,,t.s teachers and pupils, were present I'D LIS
-, >. On, latter inviting him 70 lec'uco from "iHin
ten rvant and Others Mt Frnkerstein csiis niS 'eo
itnre " an explanation OF the Pi)nc'pie py "h," w
Itoiuea the beautiful Reometrleal figures 10 "oh nave
vivs,, the name OF Magic Reeiproea@s' TINS pilhcie'
n,i,ad o,ometrlcal scope. and which is ana'ogicly
explanatory Oh the P"oN'iN0A "
Identity" -, ,,.,. ~
80, heaUtv aud symmetry, which were ARRANGED OeioIe
tbs audience Tie lecturer said; "fhe magic "oip'"
calls the symmetrical manifestations oil reoitoc u
titv demand the recognition OF force "hca n"" ~
BE- the creates. force in nature fbis iofce - INC 49,
81 ,be mower Of symmctry Chaos is without symmetry
rnass on is the striving of all elements oi h
esseuces Z, reach a final condition OF symmetry A"
commenting on the mathematical discoveries OF DE
ts. and Ieibritz Mr. Fraukensten spoke III SUBSTANCE
as follows: -, ,,.oor,.
The explanation Of reciprocal identity oy ~ G ~ i,cs
ues in ne assnciaton Of recipvOCa ntefcdah luE W d.
aud ro,nfs The point symbozcs zero ana .iS l i, ~,
nity, properties which are one 1 ,at ne lines OF
the universe Reciproestion ina,s C "a nr,cis.lv
n urr with regard 10 the points be assIo%u "a @ m Ia
as he points associated "ith fesPoo' tn n,"ts
aud lines OF Il triangle extends 10 all pow
0,ns and is this: Number Az inc VI
3 rnlvc,nn i'm Que direction around the pcrinsitr )
then BEGINNING with any lu nuueer all the nte h te
ourOsits direction. The polygun viii Ecn he coPt'eN
recnroceted Ii Will be fo nd that only the point AN
tire straight line possess the property ot fccifovdOi
No cnryr can hI reel irOcti of point cu We n'J
lie te re,ipr Ocu itself OF another curve lAc IT,
III r,,c.1 pt a circle is "a circle. The reciprocal o any
higher curye Is tt curve of IKE nature nge Ci any
kind NAV have other figures than itself for reopr"es'
bt tpy must In each ca hs Oi the same kind ol h&ue
Reeiprucsl identity meals that figure Is It's own
recgul0ca or every figure contains It's own rcPiY'aI.
After rxplaluing prucpie ~ considerable ltn+ ny
means vi diagrams aud Illustrations, the lectl or alneu
tO how the law U symmetry pcrVadcu al dui'.c
used principe of reciprocal lehtS 10
conibut DarwnisnI He said g. Draw hvc-sdcd hSufe
its reoiprsoa ie another hve-sidod figure Dtw sAN-
sidcd hgGIe, aud ITS reciprocal is III Ike hauhJ
another six-sided figure If IN each insGtnc.
We make the different sdcs eIGtl, the two uits wu
bear c. Ttam resemblance to ole another 1hey Ger
tiul. look aS much allke man and MONKEY. bGt
uIe mas five Sides and therefore individual OF It's
own tye must bdve i've sides. No fyr-siuo1 figure can
LV te renuratiye principle be converted, developed ot
forced nto the sHSdcd fUiIn any more tili monkey
can be clagCd iatO Il man. lAppatseI Man has et'i-
tanly one more side a Iuaakey He has attiibht.s
te Hokey can never pOSscsS To the end ol tlme: We
nav rest assured that tue suppJsuOn OF Que ypc ueS
chan sd mo another l. surfacc ittsltn Tue uathc-
baIieal necessity is irTevOcably against u ,
Mr. Franz nstch treated tue pruclple as Ield%u
70 fst tics IL doubtful ludny understood whdt tle
new prh G pie was AfieI he had concluded, seVefli
ma liaas present HteT tie Hctnle were eager 70
g,, trn, Air iialAcust.n clear definition O whdt hr
meant b. reciprocal" His mathematical talk was IN
te spersed with may philosophical gherdiiles, "hich
trOuOird the maJacuatcanS III following hs arSuncu'
and explanation of Reciprocal Identity AZ uathcm"1-