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admit adopted affections algebra ancients angles appears applied argument Aristotle arithmetical assume assumption axiom Barrow circle coincide Compare comparison conceive conception conclusions congruity consequence consider consistency correct defined definition demonstration difficulty direct doctrine Elements equal establish Euclid evidence example existence express extension fact fall figure former four fourth geometry given gives greater idea important impossible instance kind knowledge latter lecture less limits magnitudes mathematical means merely method mind multiple nature necessity notation notion objection once operations origin parallels particular philosophers plane Plato position possess present principles proceed Proclus produced progress Prop proportion proportionality proposition proved quantities ratio reason reference relation remark require right angles senses side simple space square straight line symbols taken term thing third tion triangle true truth universal whilst writers
Página 64 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.
Página 52 - Any two sides of a triangle are together greater than the third side.
Página 96 - ... of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth: or, if the multiple of the first be equal to that of the second, the multiple of the third is also equal to that of the fourth...
Página 122 - Whatever form is algebraically equivalent to another when expressed in general symbols, must continue to be equivalent whatever those symbols denote.
Página 17 - It is certain that from its completeness, uniformity and faultlessness, from its arrangement and progressive character, and from the universal adoption of the completest and best line of argument, Euclid's " Elements " stand preeminently at the head of all human productions.
Página 38 - Of four-sided figures, a square is that which has all its sides equal, and all its angles right angles.
Página 67 - Parallel straight lines are such as are in the same plane, and which being produced ever so far both ways, do not meet.
Página 88 - But when four magnitudes are proportionals, if the first be greater than the third, the second is greater than the fourth ; and if equal, equal; if less, less; (v.