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Page 29
... angles ; show , both by analytic and plane geometry , that it will also touch two fixed circles . 11. In an oblique - angled spherical triangle , if one side ( c ) vary , show that the corresponding variation in the adjacent angle A is ...
... angles ; show , both by analytic and plane geometry , that it will also touch two fixed circles . 11. In an oblique - angled spherical triangle , if one side ( c ) vary , show that the corresponding variation in the adjacent angle A is ...
Page 30
... angles of a plane triangle , prove sin 24+ sin 2B + sin 2C sin Asin B + sin C = 4 sin A sin B sin C , 4 cos A cos B cos C. 6. Express the area of a spherical triangle , being given two sides and the included angle . DR . SHAW . 7. From ...
... angles of a plane triangle , prove sin 24+ sin 2B + sin 2C sin Asin B + sin C = 4 sin A sin B sin C , 4 cos A cos B cos C. 6. Express the area of a spherical triangle , being given two sides and the included angle . DR . SHAW . 7. From ...
Page 31
... angles of a spherical triangle , deduce the expres- sions for the sine and cosine of half one of the sides . 10. In a right - angled spherical triangle , where C is the right angle , and A is invariable , find the change on the ...
... angles of a spherical triangle , deduce the expres- sions for the sine and cosine of half one of the sides . 10. In a right - angled spherical triangle , where C is the right angle , and A is invariable , find the change on the ...
Page 36
... angle ; construct the triangle . 12. If from either point of intersection of two circles , two right lines be drawn cutting the circles in four points , prove the lines joining these points diagonally cut at a constant angle . MR ...
... angle ; construct the triangle . 12. If from either point of intersection of two circles , two right lines be drawn cutting the circles in four points , prove the lines joining these points diagonally cut at a constant angle . MR ...
Page 38
... angle that can be cut in a given ratio by a given line . 2. Find the point on a given line from which , if perpendiculars be let fall on three other given lines , the area of the triangle determined by their feet shall be the minimum ...
... angle that can be cut in a given ratio by a given line . 2. Find the point on a given line from which , if perpendiculars be let fall on three other given lines , the area of the triangle determined by their feet shall be the minimum ...
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Common terms and phrases
acid angle Archbishop Whately argument Aristotle axis Beginning Butler calculate centre characters Church CICERO circle coefficient conic cubic curve deduce DEMOSTHENES Describe determine diameter Ending Enumerate Epistle equation equianharmonically Explain expression feet find the locus following passage force formula Give an account Greek Prose Hebrew horizontal inches inclined plane intersect length meaning Mention method mode muriatic acid original parabola passage into Greek passage into Latin passages into English perpendicular plane polar Polycarp pressure principal PROFESSOR prove radius respect right ascension right line roots Scripture sides specific gravity surface tangents temperature Thucydides tion Translate the following velocity verb Verse Version vertical weight words Write wrought iron γὰρ δὲ ἐν καὶ μὲν ὅτι οὐ πρὸς τῆς τὸ τὸν τοῦ τῷ ὡς יְהוָה
Popular passages
Page 58 - For we dare not make ourselves of the number, or compare ourselves with some that commend themselves : but they, measuring themselves by themselves, and comparing themselves among themselves, are not wise.
Page 55 - For the Son of God, Jesus Christ, who was preached among you by us, even by me and Silvanus and Timotheus, was not yea and nay, but in him was yea.
Page 57 - And herein I give my advice : for this is expedient for you, who have begun before, not only to do, but also to be forward a year ago.
Page 86 - It is the cause, it is the cause, my soul, — Let me not name it to you, you chaste stars ! — It is the cause.
Page 16 - Like a poet hidden In the light of thought, Singing hymns unbidden, Till the world is wrought To sympathy with hopes and fears it heeded not...
Page 179 - tis all a cheat; Yet, fooled with hope, men favour the deceit; Trust on, and think to-morrow will repay: To-morrow's falser than the former day; Lies worse, and, while it says, we shall be blest With some new joys, cuts off what we possest.
Page 54 - I shall see him, but not n'ow; I shall behold him, but not nigh; There shall come a Star out of Jacob, And a Sceptre shall rise out of Israel, And shall smite the corners of Moab, And destroy all the children of Sheth.
Page 290 - Therefore the Jews sought the more to kill him, because he not only had broken the sabbath, but said also that God was his Father, making himself equal with God.
Page 16 - Nor public flame, nor private dares to shine; Nor human spark is left, nor glimpse divine Lo, thy dread empire, Chaos ! is restored; Light dies before thy uncreating word : Thy hand, great Anarch, lets the curtain fall, And universal darkness buries all.
Page 55 - For all. the promises of God in him are yea, and in him Amen, unto the glory of God by us.