Miscellaneous Correspondence

Mathematical Queftions, to be answered.

Queft. 1. By Arithmetius.

Required, a general method for

Queft. 3. By Triangularius.

multiplying and dividing deci. Gangle, and the included angle,

mal fractions, and preferving exactly the decimal parts in the product or quotient, without the method of circulating numbers.

Queft. 2. By Perpendicularius. F a point be taken any where within an equilateral triangle, and perpendiculars be let fall from thence to the three fides of the triangle, the fum of these three perpendiculars will be equal to the perpendicular of the whole triangle. Quære the demonftration.

viz. AB20, BC=25, and angle B 110. To find either of the other parts of the triangle by fides and fines only, without ufing tangents or fecants, by a general theorem ?

Queft. 4. By Aftronomicus. N Lat. 5°. N°. the 1ft June 1755, what will be the fum's amplitude, and his greateft azimuth from the north?

An Elogy on Sir Ifaac Newton, tranflated from the Latin of Dr. Halley. Ehold the regions of the heay'ns furvey'd,

And this fair System in the balance
weigh'd!

Behold the law, which (when in ruin hurl'd
God out of Chaos call'd the beauteous world)
Th' almighty fix'd, when all things good he.
faw!

Behold the chafte, inviolable law!
Before us now new scenes unfolded lie,
And heav'n appears expanded to the eye;
Th' illumin'd mind now fees diftinctly clear
What pow'r impels each planetary sphere.
Thron'd in the center glows the king of day,
And rules all nature with unbounded fway;
Thro' the vast void his fubje&t planets run,
Whirl'd in their orbits by the regal fun.
What course the dire tremendous comets steer
We know, nor wonder at their prone career;
Why filver. Phoebe, meek - ey'd queen of
night,

Now flackens, now precipitates her flight;
Why, fcan'd by no aftronomers of yore,
She yielded not to calculation's pow'r ;
Why the Node's motions retrograde we call,
And why the Apfides progreffional.
Hence too we learn, with what proportion'd
force

The moon impels, erroneous in her course,
The refluent main: as waves on waves fuc-
ceed,

On the bleak beach they tofs the fea-green

weed,

Now bare the dangers of th' engulfing fand,
Now fwelling high roll foaming on the strand.

What puzzling school-men sought so long in
vain,

See cloud-difpelling Mathefis explain !
O highly bleft, to whom kind fate has given
Minds to expatiate in the fields of heaven,
All doubts are clear'd, all errors done away,
And truth breaks on them in a blaze of day.
Awake, ye fons of men, arife! exclude
Far from your breasts all low folicitude;
Learn hence the mind's ætherial pow'rs to
trace,

Exalted high above the brutal race.
Ev'n those fam'd chiefs who human life re-
fin'd

By wholesome laws, the fathers of mankind
Or they who first focieties immur'd
In cities, and from violence secur'd;
They who with Ceres' gifts the nations bleft,
Or from the grape delicious nectar preft;
They who first taught th' hieroglyphic ftile
On fmooth papyrus, native plant of Nile,
(For literary elements renown'd)

And made the eye an arbiter of found;
All thefe, tho' men of deathlefs fame, we find
Have lefs advanc'd the good of human-kind:
Their schemes were founded on a narrower