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In the oblique angle trian
C gle, (A, B, C,) the base A, B, is 16 ft;the side C, B, 11ft. and the side C, A, is 10ft, what
11 is the area. Ans. 54.3 nearly.
16+11+10=37=2=18.5 half sum. 18.5-16=2.5 first difference,
16 18.5-11=7.5 second do.
B 18.5-10=8.5 third do. The 18.5X2.5x7.5x8.5= 2948. 4375 the square root of which is 34.299 area.
Trapezium. A trapezium is a figure which has four unequal sides, and oblique angles, the area of which is found by the following
RULE. 1. Draw a diagonal line from one oblique angle to its opposite.
2. Drop a perpendicular from each of the other angles to the diagonal line, and take the length of all the lines thus formed.
3. Multiply the sum of the two perpendiculars into the length of the diagonal line, and half the product will be the
Thus:The figure, A, B, C, D, represents the trapezium. The D diagonal line, D, B, is 80 feet. The perpendicular E, C is 28ft. and the perpendicular, A, L, is
B 20 ft.; what is the area?
28+20=48X80=3840-2 -1920, Ans.
REMARKS, &c.—LESSON 8. Extracts exhibiting the correct use of allegory, Allegory. This figure may be usefully employed both in serious and instructive subjects. In former times, it was the favourite method of imparting moral and useful knowledge:of such is the nature of fable and parable.
“Thou hast brought a vine out of Egypt; thou hast cast out the heathen and planted it; thou preparedst room before itand didst cause it to take deep root, and it filled the land.
The hills were covered with the shadow of it, and the bows thereof were like the goodly cedar.
She sent her boughs into the sea, and her branches unto the river. Why hast thou then broken down her hedges, so that all they that pass by the way do pluck her? The boar out of the wood, doth waste it, and the wild boar of the field doth devour it.
Return, we beseech thee, O God of hosts!-look down from heaven, and behold, and visit this vine,--and the vineyard which thy right hand hath planted, and the branch thou didst make strong for thyself.”
"Did I but purpose to embark with thee
“No, 'tis slander,
SPELLING.--LESSON 9. ma-tu-ri-ty mā-tū'rē-tē no-bil-i-ty no-bill-le-te me-chan-i-cal mē-kă n'ê-kăl non-sen-si.cal non-sěn'sē-kä] me-dic-i-nal mē-dis'ē-năl no-vi-ci-ate no-vish'z-āte mel-lif-lu-ous měl-lif'fū-ús nu-mer-i-cal nū-měr'rik-ăl melo-di-ous mē-lo'dē-ús o-be-di-ence 7-bē'jē-ěnse men-dac-i-ty měn-dă s'ē-tē ob-li-qui-ty ob-lik'wè té : mer-cu-ri-al měs-kū'rē-ə] ob-lit-er-ate ob-lit'těr-āte me-rid-i-an mê-rid_ẽ ăn o-bliv-i-on o-bliy'vē-un me-thod-i-cał mē-thod'ê-kål ob-scu-ri-ty
ob-skū’re-tê me-ton-y-my më-tõn'ē-mê oh-se-qui-ous õb-sē'kwê-ús me-trop-o-lis me-trop pö-lis ob-ser-va-ble ob-zěr'vā-bl mil-len-ni-um mil-lēn'ne-ŭm ob-strep-er-ous ob-strēp'pěr-us mi-nor-i-ty mē-nör'e-tē OC-ca-sion-al ök-kā'zhun-al mi-nu-ti-a mē-nū'shé-ă
oc-tag-o-nal ok-tag'go-năl ini-rac-u-lous mē-răk'kū-lūs of-fi-ci-ate of-fish'ê-äte ais-an-thro-phymis-ăn’thro-pe of-fi-cious-nessöf-fish'ús-něs mmo-bil-i-ty mö.bil'le-tē om-nip-o-tenceõm-nip'pö-těnse
mo-nar-chi-cal mõ-nàr'kė-kål om-ni-sci-ence om-nish'ë-ěnse mo-nop-o-lise 'no-nop'po-lize o-pac-i-ty ö-păs'se-tê mo-not-o-nous mo-not'ó-nús op-pro-bri-ous op-pro'bre-us mo-not-o-ny mj-not'to-ne O-rac-u-lar
Õ-rak'ku-lăr anu-nic-i-pal mi-nis'ê-pål or-bic-u-lar
òr-bik'kū-lăr mu-nif-i-cence mū-nit
lê-sense o-rig-i-nal O-rij'ê-năl mys-te-ri-ous mis-tē'rê-ús or-thog-ra-phy òr-thog'grä-fe my-thol-o-gymé-thol'16-jé os-ten-si-ble
ös-těn'sé-bl ne-ces-si-ty no-sés'se-tē 0-vip-a-rous 7-vip'pa-rus sie-fa-ri-ous nē-t'ã'rē-is
pă-răb'bo-la ne-go-ti-ate né-go'shë-āte pa-ren-the-sis pā-ren'tho-sis neu-tral-i-ty nu-trál'ë-të par-ho-li-on pår-he'lē-un
LESSON 10. Jolin luin's reply, dic. continued. 6. If we fail to support this declaration of independence, it can be no worse for us. But, we shall not fail. The cause will raise up armies: the cause will create navies; the people, if we are true to them, willcarry us gloriously through the struggle. I care not how fickle other people have been found; I know the people of these colonies; and I know that resistance to British aggression is deep and settled in their hearts, and cannot be eradicated. Every colony, indeed, has expressed its willingness to follow, if we would only take the lead.
7. Sir, the declaration will inspire the people with increased courage: instead of a long and bloody war for the restoration of privileges, for redress of grievances, for chartered emunities, held under a British king, set before them the glorious object of entire independence, and it will breath into them anew the breath of life. 8.
Read this declaration at the head of the army;-every sword will leap from its scabbard, and the solem vow rise to heaven to maintain it, or perish on the bed of honour. Publish this declaration from the pulpit; religion will approve it, and the love of religious liberty will cling round it, resolved to stand or fall with it. Send this declaration to the public halls; proclaim it there; let them hear it who heard the first roar of British cannon; let them see it, who saw their brothers, and their sons fall on the height of Bunker Hill, and in the streets of Lexington and Concord, and the very walls will cry out in honour of its support.
9. Sir, I know the uncertainty of human affairs; but, I see, I see clearly, through this days business. You and I, indeed,
Be it so.
may rue it. We may not live to see this declaration made good. We may die, die, colonists,--die, slaves;--die, it may be ignominously, and on the scaffold. Be it so. If it be the will of heaven that my country shall require the poor offering of my life, the victim shall be ready at the appointed hour of sacrifice, come when that hour may.
But while I do live, let me have a country, and that a free country.
10. But, what ever may be our fate, be assured, this declaration will stand. It may cost treasure; and it may cost blood;—but it will stand, and it will richly compensate for both. -Through the thick gloom of the present, I see the brightness of the future, as the sun in the heavens. We shall make this a glorious day. When we are in our graves, our children will honour it. They will celebrate it with thanksgiving, with festivity, with bondfires, and illuminations. On its annual return, they will shed tears, copious, gushing tears, not of subjection and slavery, nor of agony and distress, but of exultation, of gratitude, and of joy.
11. Sir, before God, I believe the hour is come.judgment approves this measure, and my whole heart is in it. All that I have, all that I am, and all that I hope in this life, I an now ready to stake upon it;--and I leave off as I began, that, live or die, survive or perish, I am for the declaration. It is my living sentiment, and, by the blessing of God, it shall be my dying sentiment; Independance now, and INDEPEN
LESSON 11. ry. PARALLELOPLERON.–This is nothing more than another trapezium of a different figure. It has two parallel sides. --Being the segment of a triangle, cut off by a line drawn parallel to the base.
The area of which may be found by the Pollowing
Rule. 1. Let fall a line from either of the obtuse angles, perpendicularly to the base and find its length.
2. "Multiply half the sum of the two parallel sides, by the length of the perpendicular line, the product will be the area. Thus:In the trapezium. A, B, C,
22 221 ft
Polygram. This figure is a species of irregular polygon; it is bounded by five or more unequal sides, with as many oblique angles. The area of such figures may be found by the following
RULE. 1. Divide the figure by lines, into trapeziums and triangles as may be most convenient.
2. Find the areas of each by the appropriate foregoing rules, and the sum of all will be the answer. Thus:
Let the figure, A, B, C, D, E, F, represent a polygon,
a A divided into the trapezium, A, B, E, F, and the two angles, B, D, E, and B, C, D, then, draw the perpendicular, B, a, B c, F, F, and D.D.-And the sum of the areas of these will
D produce the true area.
9. Polygons. These are figures of from 3 to 12 or more equal sides, and of as many angles.
Their areas may be found by the following
RULE. 1. Produce a perpendicular from the centre of the given figure to the medial of either of the sides.
2. Multiply the sum of the sides by the perpendicular, ana half the product will be the area. Thus:Let the figure A, B, C, D, E,
А represent the polygon, each side of which is 16.4, and the perpendicular I, G, is 11.3. What is the area?
D G C 60-2=463.30 Ans.
Any polygon may be constructed by numerical operation, by the following
RULE. 1. Divide 360 by the number corresponding with the sides of the intended polygon.
2. Then, as the quotient is to 60, so is the side of the polye. gon required to the semidiameter of the circumscribing circle. Thus:
In a polygon of 8 equal sides, called an octagon,) each side being 7.5 inches; what is the semidiameter of the circumscribing circle? Ans. 10 in. 360-8=45. Then as, 45:60 ::7.5: 10. semidiameter,