Davidson College Notebook

1st

So glorify God is to recognize that He is, & to respond to all His will. appreciate, adore, love & obey Him.

How? By aiming at God's glory. e.g. "When [ye] give alms, do not sound a trumpet." (Pride & vain glory dis honorable & offensive as intimperences, proferring God's glory above all other things, bearing to be excelled by others, confessing sin, believing God. (he that be believeth not, maketh God a liar") – walking cheerfully, praising God.

2nd

So enjoy God is to have pleasure in His presence as our portion, "tho' our path be slippery & rough, an invisible hand holds us & guides us with wise counsel &, after shame & wretchedness, [lead] us in honor & glory to the place, where we shall be received by Him who was our highest good on earth", seeing God as He is when we are like Him, the 27th Psalm. "Let those refuse to sing, who never knew our God, But favorites of the heavenly King may [sheak] His praise [sbrased]"

My God, the shining of all my joys, The life of my delights, The glory of my brightest days And comfortcomfort of my nights!

73

A Key to Davies' Algebra; commencing with Equations of the first degree: beginning on the 73^rd page By Rolf Z. Johnston, July 29th 1853

Beginning with the 8^th sum on 73 pag Let x-Bx amount Thus x+x+x=1000+144+100 x + 72 = A's So 3x = [-756] = 252 B's x + 72 + 100 = C's And 252 + 72 = 324 A's &c

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9^th sum Let x = B's Share x + 84 = A's, when he sits down x + 48 x 5 = A's wining x + 84 = -5x + 240 = x + 5x = 240 - 84 = 6x = 156/6 = $26 Answer

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10^th sum Let x = The amount of his property (1/2)x = The wife share (2/6)x = The daughter's share (1/12)x = The servant's share Let v = The poor's share

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[figure]

The figure is designed to show that the center of the sphere is taken in the grown line, in the Extra of the XV problem of the VI chapter of Davis Discription Geometry.

March 20th 1856 D. College N.C.

R.Z. Johnston

Contents

	Page
Consideration worthy a student's attention	6th
Loquacity	4th
Silence	2d
Bailley & St. Barnard's dying legacies	3
[Reading] & The Study of Mathematics	5
Reproach upon Education	7
Time, Consideration, General Character	8
Wisdom	1
[A ??ation] for the formation of character	9
A sublime sentence	10
Business of a scholar.. How to live	11
Education	12
Insufficiencies of human Enjoyments	13
Eloquence	14
Oratory	15
Wealth, no pretext for Indolence	16th
Picture of Life	17th
[Weyar's] letter to America	18th
[Tenth Parting]	22d
How Babylon was destroyed	23d

1st

1855 {June 16th} Bias when he came to die, bequeathed this instruction to those who survived him: "That they should so order their lives as if they were to live a very little, and a very great while". From which principle of his, his {Wisdom} friend Cleobulus on his death-bed inferred this conclusion: "That those men only live to any purpose, who overcome carnal pleasures, make virtue familiar, and vice a stranger to their souls; the great rule of life, as he observed, being to be moderate, and, the great work of it to meditate, according to the remark of his contemporary Periander, who [heated] pleasure which were not immortal; leaving behind him this axiom, [ Mελέτη, Τo Πà?]: "Meditation is everything."

See Dodd's Lectures to Young Men, on Anecdotes to recommend an Early Appreciation to Wisdom, Page 99

14

And who would wish possessed, What all must scorn or rue? Then pass by beauty with looks above; Oh! seek never - share never - woman's love!

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I find now, what I have always felt, that a sick bed is no place to prepare for eternity. But I have not that to do. I long ago made my peace with God. The God I have [feebly] feebly preached to others is my support. — See Memoirs of Dr. Sampson. The above were his sentiments on his death-bed.

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"Proprium humani ingenii est, odisse quem laeseris" (See [Tac vit Agric] Ch XLII)

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There are now in the United States 144 Colleges, and 46 Theological Institutes; and 400000 youths in school. Feby 26th 1857

15

Analytical Geometry

Page 21. Example 1) horizontal line Right triangle abc with line from point b to the hypotenuse Let b = The base of the triangle Let d = the difference Let x = the hypotinuse Let x-d = the perpendicular

We know b = [square root]x²-(x-d)²; or b[/square root] = [square root]x²-(x²-2dx+d²)[/square root]; or [squaring] both numbers b²=x²-x²+2dx-d²; or 2dx=b²+d²; or x = (b²+d²)/(2d) horizontal line

(Exm. 2) Rectangle defh with area x is inscribed in triangle abc, which has a height of h.

Let ab' = Area of the triangle Rectangle Let x = Less side of the rectangle [therefore] ab = Greater side of the rectangle b = The base of the triangle h = altitude

Then we have b:h::(ab')/x:h-x; hence bh-bx = (ahb')/x; or bhs-bx² = ahb; or bx²-bhx = -ahb'. Solving we have bx²-bhx+((^bh)/2)²; or x²-hx+(h/2)² = -ahb'/b + (h/2)² x = h/2 ± [square root](h/2)² - ab'h/b[/square root]

16 Analytical Geometry Page 31

(Exm 3) Circle with radius R is inscribed in triangle abc

Let P = The perimeter of the triangle [Let] R = [The] radius of the inscribed circle [Let] x = [The] altitude of triangle [Let] y = [The] base [of triangle]

Then, since the area of a triangle is equal to its perimeter into half the radius of the inscribed circle, (Book B. Prop IX) we have this equation , or xy = Pa, [never] y = Pr/x

But P = x + y + ; or ; and squaring x² + y² = P² - 2Px + 2xy - 2Py + x² + y²; or 2 Px - 2xy = P² - 2Py; or (2p - 2y)x = P² - 2Py: hence x = . Now substituting Pr/x for y; and we have . [Or] we have 2Px² - 2Prx = P²x - 2P²r or P(2x² - 2rx - Px) = -2Pr) or or or or

22

[Ana Grom]. Four methods for constructing a strait line

1st: By a series of points: i.e. assuming [volms] for x or y

2nd: Making x or y = 0, and finding the other

3rd: By means of the Tangent which the line makes with x

4th: Solving with respect to x, and there by means of the Tangent, which the line makes with axis of y

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Problems in Calculus (Page 98)

diagram of triangle with inscribed rectangle

(4th Example) = Let x = one part u = x^m(a-x)ⁿ [Let] a-x = other

du/dx = mx^m-1(a-x)ⁿ-nx^m(a-x)^n-1 = x^m-1(a-x)^n-1(m(d-x)-nx) = ma-mx+nx + m(a-x)-nx = 0

= Ans

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5th Ex... Let a = Altitude of triangle [Let] b = Base " " " x = Altitude of rectangle " y = Base " " ∴ xy = Area of [rectangle]

b:a::y:a-x, ∴ ay = ba-bx & xy = u = = b/a(ax-x²)^a Neglecting the constant b/a, we have du/dx = a-2x = 0, x = a/2 = Ans.

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6th Ex. diagram of a cylinder Let x = Altitude, y = Radius of Base, Solidity (s) = πy²x,

Surface of cyclinder (n) = 2πxy + πy² = + πy² = 2s/y + πy² =

πy³ - s = 0 =

πy²x = πy³, divide by πy², and we have x = y = Ans.

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7 Ex. diagram of a circle with inscribed rectangle Let a = Radius of circle, x = Alt of rectangle, y = Base of [Do]

n = xy = area of rectangle

4R² - 2y² = 0 2R² - y² = 0

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Good Remarks & Proverbs

Miracles: A miracle does not prove the truth of a doctrine or the divine mission of him that brings it to pass. The doctrine must first commend itself to the conscience as being good, truly then can the miricle seal it as divine. [French]

Man is not only unable to realize the perfect, he is unable to conceive it. The idea is as much a gift as the power to realize that idea. [French]

The Church: The wonder of the existence & subsistence of the Church in the world is itself so great that to believe or not to believe the miracles is only choosing an alternative of wonders. If you do not believe the miracles, you must at least believe this miracle, that the world was converted without miracles. Augustine

Nature: Nature is but the outward expression of the will of God. God cannot be contrary to God. Augustine

God Symonides, when asked by [Hero] king of Sicily "Who God was" requested at first one, then two, three & even four days, to think of the question & finally answered, "The more I reflect on the subject, the more I am convinced of my own ignorance."

Natural Sense of Religion There has never been a State of atheists. If you wander over the earth, you may find cities without walls, without kings without [mint], without theatre or gymnasium, but you will never find a city without a God, without prayer without oracle, without sacrifice. Sooner [?] a city stand without foundations, than a State without belief in the Gods. This is the bond of all society & the pillar of all legislation." Plutarch, in reply to the Epicurean

Revelation Thus it has ever been with the revelation of the divine. What it does not draw to itself it drive from itself, what it does not win to obedience it arrays in active hostility. So it was clearly manifested in the Jews, who found fault with Christ in the case of the "Important man" John VI-16