Bapu Deva Sastri Bhāskarācārya.

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tion, as to liow tho Earth of the Sun and of Fire, as cold of the
has ita own inherent power. „ » -».

Moon, flmdity of water, and hardness

of stones, and as the Air is volatile, so the earth is naturally
immoveable. For oh I the properties existing in things are
wonderful.

G. 'Jlio* property of attraction is inherent in tho Earth.
By tills property the Earth attacts any unsupported heavy
tiling tow<u*ds it : Tho thing appears to bo falling [but it is in
a state of being drawn to the Earth] . The etherial expanse
being equally outspread all around, where can the Earth fall ?

Opinion of the Baud. ^- Observing the revolution of the
DHAs. constellations, the Bauddhas thought

that tho iSartli hml no siippoiii, and as no heavy body is soon
stationary in the air, they asserted that the earthf goes eternal-
ly downwards in sptice.

. . , 8. TTie Jainas and others maiu-

Opuiion of the Jiinas. . , , « t

tain that there are two Suns and two

* [It is manifest from this that neither' can the Earth hy any means fall
downwards, nor the men situated at tlie distances of a fourth part of the circum-
ference from us or in the opposite hemisphere. B. D.]

t [Ue who resides on the Earth, is not conscious of the motion of it down-
wards in space, as a man sitting on a mo? ing ship does not perceive its motion,
B. D.]



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114 Translation of the [III. 9.

Moons, and also two sets of constellations, which rise in con-
stant alternation. To them I give this appropriate answer.

Refutation of the opmion ^' Observing as yon do, O Baud-
of the BiDDunAs. dha, that every heavy body projected

into the air, comes back again to, and overtakes the Karth,
how then can you idly maintain that the Earth is falling down
in space ? [If true, the Earth being the heavier body, would,
he imagines* — perpetually gain on the higher projectile and
never allow its overtaking it.]

Refutation of the opinion 10. But what shall I say to thy

of the JAiHAa. fouy^ Jaina, who without object or

use supposest a double set of constellations, two Suns and two
Moons ? Dost thou not see that the visible circumpolar con-
stellations take a whole day to complete their revolutions ?

Refutation of the BuppoBi- 1 1 . If this blessed Earth were level,
tion that the Earth is lerol. jj^^ ^ pj^^ mirror, then why is not the

sun, revolving above at a distance from the Earth, vinible to

men as well as to the Gods? (on the PAUfti(NiKA hypothesis,

that it is always revolving about Mebu, above and horizontally

to the Earth.

12. If the Golden mountain (Mebu) is the cause of night,

then why is it not visible when it intervenes between us and

the Sun ? And Mbbu being admitted (by the Paubanikas) to

lie to the North, how comes it to pass that tho Sun rises (for

half the year) to the South ?

, . . , ■ 13. Ab the one-hundredth part of

Reason of the false ap- , . ^ ^

pearanoe of tho plane form the Circumference of a circle is (scarce-

ot the Earth, j^ ^^ff^^^^^ fr^^j ^ p,^^^ ^^ ^

the Earth is an excessively large body, and a man exceedingly
small (in comparison,) the whole visible portion of tho Earth
conseG[uently appears to a man on its surface to be perfectly
plane,

* [This was ])nA8KABA*8 own notion i— but oyon on the more corrcot priuciplo,
lUtt^ all boilioa fall with equal rapidity, the arguuiont holds good. ii. P.J



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III. 18.] Sidhdnta-g'ironmnL 115

^ ^ ^.. . ^ 14. That the correct dimensions of

Proof of tlie correctness of

alleged circutnferonce of the the circumference of the Earth have
been stated may be proved by the
simple Bole of proportion in this mode : (ascertain the diifdt*-
ence in Yujanas between two towns in an exact north and
south line^ and ascertain also the difference of the latitudes of
those towns : then say) if the difference of latitude gives this
distance in Yujanas, what will the whole circumference of 360
degrees give ?
To confirm the same oir- 16* As it is ascertained by calcula-

cumference of the Earth. ^^^ ^j^at the city of UjJATINf is

situated at a distance from the equator equal to the one-sixteenth
pjvrt of the whole circumforouco : this distance, therefore,
multiplied by 16 will be the measure of the Earth's cir-
cumference. What reason then is there in attributing (as the
PaurXnikas do) such an immense magnitude to the earth 7

16. For the position of the moon's cusps, the conjunction
of the planets, eclipses, the time of the risings and settings
of the planets, the lengths of the shadows of the gnomon,
&c., are all consistent with this (estimate of the extent of the)
circumference, and not with any other ; therefore it is declared
that the correctness of the aforesaid measurement of the earth
is proved both directly and indirectly, — (directly, by its
agreeing with the phenomena ; — ^indirectly, by no other estimate
agreeing with the phenomena).

17. LankX is situated in the middle of the Earth : Yama-
KOTi is situated to the East of Lanka, and Romakapattana to
the west. The city of Siddhapura lies underneath LankX.
SuMRUir is situated to the North (under the North Pole,) and
VadavInala to the South of LankX (under the south Pole) :

18. These six places are situated at a distance of one-fourth
part of the Earth's circumference each from its adjoining one.
So those who have a knowledge of Geography maintain. At
Meru reside the Gods and the Siddhas, whibt at Yadav^nala
are situated all the hells and the Daittas.

c 2



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116 Translation of the [III. 19.

19. A man on whatever part of the Globe he may be,
thinks the Earth to be under his feet, and that he is standing
up right upon it : but two individuals placed at 90* from each
c^her, fancy each that the other is standing in a horizontal
line, as it were at right angles to himself.

20. Those who are placed at the distance of half the
Earth^s circumference from each other are mutually antipodes,
as a man on the bank of a river and his shadow reflected in
the water : But as well those who are situated at the distance
of 90' as those who are situated at that of ISO* from you, main-
tain their positions without difficulty. They stand with the
same ease as we do here in our position.

PoBitioDB of tho DwfPAB 21. Most learned astronomers have
and Seat. stated that jAMBtJDwf PA embraces the

whole northern hemisphere lying to the north of the salt sea :
and that the other six DwfPAS and the (seven) Seas viz.
those of salt, milk, &c. are all situated in the southern hemis-
phere.

22. To the south of the equator lies the salt sea, and to
the south of it the sea of milk, whence sprung the nectar,
the Moon and the Goddess LAKSHMf, and where the Omni-
present YXsunEVA, to whose Lotus-feet BrahmX and all the
Gods bow in reverence, holds his favorite residence.

23. Beyond the sea of milk lie in succession the seas
of curds, clarified butter, sugar-cane-juice, and wine: and,
last of all, that of sweet Water, which surrounds VADAVifNALA.
The Pirihk LoKAS or infernal regions, form the concave
strata of the Earth.

24. In those lower regions dwell the race of serpents (who
live) in the light shed by the rays issuing from the multitude
of the brilliant jewels of their crests, together with the multi-
tude of AsuBAS ; and there the Siddbas enjoy themselves
with the pleasing persons of beautiful females resembling the
finest gold in purity.

25. The S'iKA, S'^lmala, Kaus'a^ EbjCukcha, Gomkdaka, and



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III. 31.] SUlhanta-sirmnanL 117

PusHKARA DwfrAS OTG Situated [in the intervals of the above
mentioned seas] in regular alternation: each Dwipa lying,
it is said, between two of tlipse seas.

Positions of the Monn- 26. To the North of Lank! lies
u;"'le'THt«v:i'V"u *« HiMiLATA moutttain, and beyond
caused by the mountains. that the HsMAKtJTA mountain and
beyond that again the Nisuadha mountain. These three
Mountains stretch from sea to sea. In like manner to
the north of Siddhapura lie in succession the S'^lingavXn
S'uKLA and NfLA mountains. To the valleys lying between
these mountains the wise have given the name of Varshas.

27. This valley which we inhabit is called the BhArata-
VARSiiA; to the North of it lies the Kinnaravarsha, and
beyond it again tlie Harivarsha, and know that the north
of Siddhapura in like manner are situated the Kuru, Hira^-
MATA and Bamtaka Varshas.

28. To the north of Yamakoji lies the MalyavXn mountain^
and to the north of Bomakapattana the Gamdhamadana
mountain. These two mountains are terminated by the NfLA
and NisuADUA mountains^ and the space between these two
is called the iLivJCiiTA Varsha.

29. Tlie country lying between the MalyavXn mountain
and the sea^ is called the Bhadraswa- varsha by the learned ;
and geographers have denominated the country between the
GAMDHAMiCDAMA and the sea, the KetumXla- varsha.

30. The Ilavj(iita-varsha, which is bounded by the
NiSHADiiA, NfLA, Gandhamadana and Malyavan mountains, is
distinguished by a peculiar splendour. It is a land rendered
brilliant by its shining gold, and thickly covered with the
bowers of the immortal Gods.

Position of the mountain 31 . In the middle of the IlXvj^ita
MuEuinlLlT^iTA. Varsha stands the mountain Mbru,

which is composed of gold and of precious stones, the abode
of the immortal Gods. Expounders of the Pur&nas have
further described this Mbru to be the pericarp of the earth-
lotus whence Brahma had his birth.



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1 1 8 Translation of the [III. 32.

32. The four mountains Mandara, Suqandha, Vipula and
SupXrs'wa serve as buttresses to support this Mbru, and upon
these four hills grow severally the Kadamba, JAMUtJ, Vaja
and PiPPALA trees which are as banners on those four hills.

33. Prom the clear juice which flows from the fruit of the
Jamd(j springs the jAMBtJ-NAnf ; from contact with this juice
earth becomes gold : and it is from this fact that gold is
called jAHDtJNADA : [this juice is of so exquisite a flavour that]
the multitude of the immortal Gods and Siddhas, turning
with distaste from nectar, delight to quafl^ this delicious
beverage.

34. And it is well known that upon those four liills [the
buttresses of Mbru] are four gardens, {Ast) Chaitraratha
of varied brilliancy [sacred to Kubbra], i^nd) Nandana
which is the delight of the Apsaras, (3nQ the Diiiiiti which
gives refreshment to the Gods, and {4itU) the resplendent
VaibhRi^ja.

35. And in these gardens are beautified four reservoirs,
viz. the Aruna, the MiCMASA, the Mah^hrada and the S^weta-
JALA, in due order : and these are the lakes in the waters
of which the celestial spirits, when fatigued with their
dalliance with the fair Goddesses, love to disport themselves.

36. Mbru divided itself into three peaks, upon which are
situated the three cities sacred to Vishnu, Brahm/^ and S'iva
[denominated Vaikuntha, Brahmapura, and Kailasa], and
beneath them are the eight cities sacred to Indra, Agni, Taha,
Nairrita, Varuna, V^yu, S'As'f, and Is a, [i. e. the regents
of the eight Dues or directions,* viz., the east sacred to

* [As the point whero the equator cnti the horison is the east, the sun
therefore rises due east at time of the equinoxes but on this ground, we
eannot determine the direction at MtBU [the north pole] because there the
equator coincides with tlie horizon and consequently the suu moyes at Miuu
under the horison the whole day of the equinox. Tet the ancient astronomers
maintained that the direction in which the tamakoti lies from Msuu is the
east, because, according to their opinion, the inhabitants of Mbuu saw the
sun rising towards the TAMAKafi at the beginning of the kalpa. In the same
manner, the direction in which LahkA lies from mount Mkuu is south, that
in wliioh Bomakafattana lies, is west, and the direction in which Siddua-



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III. 40.] SidJidnta'a'iraniani. 119

Indra, the south-east sacred to Agni, the south sacred to
Yama, the south-west sacred to Nair^ita, the west sacred to
Varuna, the north-west sacred to Vayu, the north sacred to
S'as'f and the north-east sacred to fs'A.]
Some peculiarity. ^^^ The sacred Ganges, springing

from the Foot of Vishnu, falls upon
mount Mbru, and thence separating itself into four streams
descends through the heavens down upon the four Vishkam-
BHAS or buttress hills, and thus falls into the four reservoirs
[above described] .

38. [Of the four streams above mentioned], the first
called SfTA, went to Bhadras'wa-vabsha, the second, called
Ai^kananpX, to UhXrata-varsha, the third, called Chakshu,
to KktumXla-varsua, and the fourth, called BhadrA to Uttara
KuRU [or North Kuru] .

39. And this sacred river has so rare an efficacy that if
her name be listened to, if she be sought to be seen, if seen,
touched or bathed in, if her waters be tasted, if her name
bo iittK)r(Ml, or broii^rht to mind, and hor virtues bo colobnitod,
she purilios in many ways thousands of sinful men [from
tlioir sins] .

40. And if a man make a pilgrimage to this sacred stream,
the whole line of his progenitors, bursting the bands [imposed
on them by Yama], bound away in liberty, and dance with
joy ; nay even, by a man's approach to its banks they repulse
the slaves of Yama [who kept guard over them], and, escaping
from Naraka [the infernal regions], secure an abode in the
happy regions of Heaven.

FUBA lies from Mbbtj is north. The buttresses of Mbbit, Mavdaba, Suoakdha,
&c. are situated in the east, south &o. from Mbbit reepectiTelj. B. D.J

Note on rerses from 21 to 43 t^fi RASKABa'oha'bta has exercised his ingenuity
\n giving a locnlitv on tho earth to the poetical iinaginalions of Yta'ba, at the
same tinio that he hus preserved his own principles in regard to the form and
dimensions of the £arth. But he himself attached no credit to what he has
described in those Terses for he concludes his recital iu his commentarj with
the words,

** What is stated here rests all on tho authority of the PUBXtris."
As much OS to sajr " crodat Judsuus*" L. W«



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120 TniMlation of the [III. 41.

The 9 .Hi»piB and 7 ^^- ^«™ ^"^ ^^'^ BH/fRATA-VAE8HA

KviUoBALAB ot Bha'bata- aTO embraced the followinir nine khan-

VAR8HA

PAS [portions] viz. Aindha, Kas'kru,

TamRAPARNA, GaBHASTIMAT, KuMARIKA^ NAQA, SaUMYA, ViRUNA,

and lastly GiNDHARVA.

42. In the KumjCrika alone is found the subdivision of
men into castes ; in the remaining kuanpas are found all the
tribes of Antyajas or outcaste tribes of men. In this region
[BhjCrata-varsha] are also seven kulXchalas^ viz. the mahen-
DRA, S UKTi, Malaya, Hiksiiaka, rXitiYATiiA, the Sauya, and

ViNDHYA hills.

Arrangement of the seven 43. The country to the SOuth of

LoKAfl worlds. ^YiQ equator is called the BntiRLOKA,

that to the north the Bhuvaloka and Mbru [the third] is
called the Swarloka, next is the Mauauloka in the IToavous
beyond this is the Janaloka, then the Tapotx)ka and last of
all the Satyai/>ka. Those IiOKAB are gradually altaiuod by
increasing religions merits.

44. When it is sunrise at LankX, it is then midday at

Yamakoti (90^ east of LankX), sunset at Siddhapura and

midnight at Romakapattana.

-. . ^ . ,, 45. Assume the point of tho

Points of the compass '

whj Mbbu is due north of horizon at wliich the sun rises as
^ * tho oast point, and that at which ho

sets as the west point, and then determine the other two
points, i. e., the north and south through the hatsya'I' effected
by the east and west points. The line connecting the north
and south points will be a meridian line and this line in
whatever placo it is drawn will fall upon tho north point :
hence Mkru lies due north of all places.

A curious fact is rehearsed. 46. Only Yamakoti lies due east
Geograpbicd Anomalj. f^^^ UwAYinf, at the distance of 90«

* [From the east and west points, as centres, with a common radius describe
two area, intersecting each other in two points, the place contained bv the
arcs is called Matsta ** a fish" mid the iuterseotiug poinu are the north and
south points. B. D.j



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III. 51.] Sidhdnta-s'ironiani. 121

from it : but Lanka and not UjJAYiNf lies duo west from
Yamakoti.

47. Tho samo is the case everywhere ; no pkce can lie west of
that which is to its east except on the equator, so that east
and west are strangely related.*

48. A man situated on the equa-^
tor sees both the north and south
polos touching [tho north and south points of] the horizon,
and the celestial sphere resting (as it were) upon the two
poles as (Centres of motion and revolving vertically over his
head in the heavens, as the Persian water-wheel.

49. As a man proceeds north
from tho equator, ho obsei*vos tho
constellations [that revolve vertically over his head when
seen from the equator] to revolve obliquely, being deflected
from his vertical point : and the north pole elevated above
his horizon. The degrees between the polo and the horizon
ai-e the degrees of latitude [at the place]. These degrees
are caused by tho Yojanas [between tho equator and tho
pbvco] .

How tiio dogrooB of IMi. 50. Tlio number of Yojanas [in
iiido iiro jjrodujjod from ilio ^j^^^^ ^^.^ ^f ^^^^ terrestrial or celestial

diataiico m YoJANAS and -^ . . , ^

Tioo rersA. circle] multiplied by 360 and divided

by [the number in Yojanas in] the circumference of the
circle is the number of degrees [of that arc] in tho earth
ov in tho planetary orbit in tho heavens. The Yojanas ai-e found
from tho degrees by reversing the calculation.

51. The Gods who live in tho
rorallol Bphoro. mount Mbbu observe at their zenith

[• As tho sun or any lioavonly body when it roaclio* tlio Prime Vortical
of any place is caUcd due east or west, so according to the Uindu Astronomical
hniguoKO aU the places on tho Earth which are situated on the circle
oor^|K)nding to tho Prime Vortical arc due east or west from the place and not
those which are situated on the parallel of Utitude of the place, that is the
places which have the angle of position 90« from any place are duo oast or
west from that place. And thus nil directions on the Earth are shown by
means of tho angle of [wsilion in tho Uindu Astronomical works. U. U.J

1)



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1 22 Translation of the [III. 52.

tho north polc^ wliilo tho Daityas in Vadav^Cnala tho south
pole. But while the Gods behold tho constellations revolving
from left to right, to the Daityas they appear to revolve from
right to left. But to both Gods and Daityas the equatorial
constellations appear to revolve on and correspond with the
horizon.

Dimensions of the Earth's 52. The circumference of the earth
oiroumference. j^^ ^^^ pronounced to be 4967

YojAKAS and the diameter of the same has been declared to
be 1581yV YojANAS in length : the superficial area of tho Earth,
like the nfet enclosing the hand ball, is 78,53,03 1 square
YojANAS, and is found by multiplying the circumference by
the diameter.*

Tl..errorofLall.5..x. ^3. The Superficial area of the

posed in regard to the super- Earth, like the net enclosing tho

ficial area of tho liorth. i t i n . ^ i i^ ^ i

hand ball, is most erroneously stated

by LALiiA : tho true area not amounting to one hnndrodth
part of that so idly assumed by him. His dimensions are
contrary to what is found by actual inspection : my charge of
error therefore cannot be pronounced to be rude and uncalled
for. But if any doubt be entertained, I beg you, learned
mathematicians, to examine well and with tho utmost impar-
tiality whether the amount stated by me or that stated by
him is the correct one. [The amount stated by Laujv in his

* [The diameter and the ciroamferencd of the Earth here mentioned are to
^eaoh other as 1250: 8927 and the demonstration of this ratio is shown hj
BaXsKABioEXBTA in the foUowinff manner.

Take a radius equal to anj urge number, suoh as more than 10000, and
through this determine the sine of a smaller arc than eren the 100th part of
the oiroumferenoe of the oirole by the aid of the canon of sines (Jyotpatti,)
and the sine thus determined when multiplied by that number which represents
the part which the arc just taken is of the ciroumferenoe, becomes the length of
circumference because an arc smaller than the 100th part of the oiroumferenoo
of a circle is [scaroelj dilTerent from] a straight line. For this reason, the cir
oumferenoe equal to the number 62882 is granted by ABTiDniTTA and the others,
in the diameter equal to the number 20,000. Though the length of the circum-
ference determined by extracting the square root of the tenfold square of the
diameter is rough, yet it is grants for conyenienoe by SbiduauAoha B7a, Braii-
jf AQUPTA and the others, and it is not to bo supposed that they wore ignorant
of this roughness.— -B. 1).]



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III. 59.] Sidhdnia'S'ironiani, 123

work entitled Dnfvj[iiiDDiriDA-TANTEA is 285,63,38,557 square
YojANAS, which he appears to have found by multiplying the
square contents of the circle by the circumference.]

Shows the wrongneis of 54. If a piece of cloth be cut in
the Bule given bj Lallii. ^ circuhu- form with a diameter equal

to half the circumference of the sphere, then half of the sphere
will be (entirely) covered by that circular cloth and there will
still be some cloth to spare.

55. As the area of this piece of cloth is to be found nearly
24 times the area of a great circle of the sphere : and the
area of the piece of cloth covering the other half of the sphere
is also the same ; *

50. Therefore the area of the whole sphere cannot be more
than 5 times the area of the great circle of the sphere. How
then has he multiplied [the area of the great circle of the
sphere] by the circumference [to get the superficial contents
of the sphere] ?

57. As the area of a great circle [of the sphere] multiplied
by the circumference is without reason, the rule (therefore of
JjAiiiiA for the sajwrficial contents of the sphere) is wrong,
and the superficial area of the Earth (given by him) is conse-
quently wrong.

Otherwise. ^^' ^^' Suppose the length of the

[equatorial] circumference of the globe
equal to 4 times the number of sines [viz. 96, there being 24
sines calculated for every 3®f , which number multiplied by
4 = 90] and such oblong sections equal to the number of the
length of the said circumference and marked with the vertical
lines [running from pole to pole], as there are seen formed by
nature on the Xnwl J fruit marked off by the lines running
from tho top of it to its bottom.

* Let the diameter of a sphere be 7 : the circumrerenoe will be 22 nearly.
The area of a circle whose diameter is 7 will be about 88 1 ; that of a circle
whose diameter is 11 (^ oircomferenoe) will be about 89} tliis 89 J is little less
than2| times 88|. L. W.

D 2



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121.



Translation of (he



[Til. CO.



CO. If wo dotcrmino the superficial area of one of tlioso
sections by means of its parts, wo have it in this form. Sum of
all tho sines diminished by half of the radius and divided by
the same.*

* The correctness of this form is thus briefly illustrated by BaA'sKABA^onA'sTA
in his commentary.

heigaha^ff be tho section in which ah, h o,e d &c.
and aj>i, b^c^, c,(fi, &o. are each equal to 1 cubit and
also aa^ arc equal to 1 cubit : then bb^, ce^, dd^^ &c.
are proportional to the sines mb^no^ od^ &c. and are
thus found.

mb.

If Ira or rad : give, aa 1 (= 1) : : m5 ; bb^ =

Had.

ne

If Bad 1 1 : : no : cc, = —

Mad

od

again Bad : 1 : iod:dd^:=

Mad
Ac.
Now ai»|, bb^t 00„ &0. being found, the contents of
each of aa^ bjt, Ib^ o,o, oo^ d^d, ko, the part of tho
Hoction is found by taking half the sum of aet^ & bb^
hh^ k coy^ C0, k dd^ ko. and multiplying it by ab
(which is equal to cnch of bo, cd, Ac.) hero ab is assumed ns 1 and tho wholo
surface each of aajt^b^ W,o,c as a plane, for an arc of U«4 b scarcely diiroroiit
from a plane.

Now to find the sum of aajf^b, bb^e^e ko, we hare

a^t + bb, bb.^co, ee, + dd,

' — ;; — ^ ^ + — : — x ^ + x i + &c.

adding these and leaying out 1 multiplier, we haye

iaa, + bb, + co, + dd,^kc.
„ W„ Ac.




. we have



Substituting the Talues of aa
mb no od
1 + — H + — 4- &0. so on for tho as8nmo<l sines

ji :r H

but I = =

It It B

By substitution we get

It mb me

-—+—-+ + ko.

It It It

n + mb + n0 + od^ko,. —ilt



J2



It is endent from this that the sum of all the sines diminished by the half
of the Badius and dirided by the Badius is equal to the contents of tho upper


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