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...le ''BAC'' is [[Right angle (geometry)|right]] (unless ''C''=''A''), see [[Pythagorean theorem]] (orthogonality is not only sufficient but also necessary for the equality

...le ''BAC'' is [[Right angle (geometry)|right]] (unless ''C''=''A''), see [[Pythagorean theorem]] (orthogonality is not only sufficient but also necessary for the equality

Another famous proposition in Book I is number 47: the [[Pythagorean theorem]], which is proved by a technique still used in high school texts. This is

where, by the [[Pythagorean theorem]],

...Trigonometry]] combines space and number, and encompasses the well-known [[Pythagorean theorem]]. The modern study of space generalizes these ideas to include higher-dim

...''h'' and the other side half the distance traveled, say ''L''/2. By the [[Pythagorean theorem]], the hypotenuse must be greater than ''h'', in fact {{nowrap|√(''h''<su