 | Elias Loomis - Conic sections - 1858 - 256 pages
...angles DBA, ABE, EBC. Now things that are equal to the same thing are equal to each other (Axiom 1) ; therefore, the sum of the angles CBA, ABD is equal...to the sum of the angles CBE, EBD. But CBE, EBD are two right angles ; therefore ABC, ABD are together equal to two right angles. Therefore, the angles... | |
 | Religion - 1858 - 806 pages
...Christ was the " son of David ;" hence were Solomon and Christ the one or parallel characters, for things which are equal to the same are equal to one another. If the " last days " were to be the days of Christ, and if those were to be as the " days of Noah,"... | |
 | James Yates - Decimal system - 1858 - 100 pages
...differences must exist in all attempts to compare the lengths of different objects. Euclid's axiom, " Things, which are equal to the same, are equal to one another," is strictly true only of mathematical lines and other imaginary quantities. In practice it is sufficient,... | |
 | 1858 - 812 pages
...David;" Christ was the "son of David;" hence were Solomon and Christ the one or parallel characters, for things which are equal to the same are equal to one another. If the " last days " were to be the days of Christ, and if those were to be as the " days of Noah,"... | |
 | Eucleides - 1860 - 396 pages
...are equal to one another in area. CONSTRUCTION. — Draw BE and CH. DEMONSTRATION. Syllogism 1. Da (Things which are equal to the same) ARE equal to one another. [Ax. 1.] ii The straight lines BC and EH ARE equal to the same FG. [Hypoth. and I. 34] i Therefore... | |
 | James McCosh - History - 1860 - 512 pages
...as the " Common Notions," so far as they relate to quantity, prefixed by Euclid to his Elements. " Things which are equal to the same are equal to one another." " If equals be added to equals, the wholes are equal." " If equals be taken from equals, the remainders... | |
 | Euclides - 1860 - 288 pages
...been shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another; therefore the straight line to BC. Wherefore from the given AL shall line AL BC. AL is equal point A a straight has... | |
 | Medicine - 1862 - 792 pages
...insisted on by Mr. Lewes and others : namely, that alcohol replaced a certain amount of food ; and " as things which are equal to the same are equal to one another," he inferred that if a glass of ale was equal to a slice of mutton, in its satisfying effect, and that... | |
 | George Ramsay - Instinct - 1862 - 160 pages
...in the first place, what are called the Axioms of Mathematics or the Science of Quantity, such as " Things which are equal to the same, are equal to one another." " If equals be added to equals, or subtracted from equals, the wholes, or the remainders, will be equal."... | |
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Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term. 
