The Russians, they say, fortified this position in advance on the left of the highroad (from Moscow to Smolensk) and almost at a right angle to it, from Borodino to Utitsa, at the very place where the battle was fought.

The case was evidently this: a position was selected along the river Kolocha--which crosses the highroad not at a right angle but at an acute angle--so that the left flank was at Shevardino, the right flank near the village of Novoe, and the center at Borodino at the confluence of the rivers Kolocha and Voyna.

The east and west walls should run parallel to each other, and at right angles to that on the north side, in all the most favoured localities; but in colder or later ones, though parallel, they should be so far removed from a right angle as to get the sun by eleven o'clock.

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Not only did the Russians not fortify the position on the field of Borodino to the left of, and at a right angle to, the highroad (that is, the position on which the battle took place), but never till the twenty- fifth of August, 1812, did they think that a battle might be fought there.

If these lines be turned through a right angle in the same sense, they take up positions such as CC, DID, where C, D are on JC, JD, respectively, and CD is parallel to CD.

To the west of Parr's Ridge the surface for the most part slopes gently down to the east bank of the Monocacy river (which flows nearly at a right angle with the streams east of the Ridge), and then from the opposite bank rises rapidly toward the Catoctin Mountain; but just above the mouth of the Monocacy on the east side of the valley is Sugar Loaf Mountain, which makes a steep ascent of 1250 ft.

The difference between an acute angle and a right angle is termed the complement of the angle, and between an angle and two right angles the supplement of the angle.

Leaving the right angle out of consideration, the sides including the right angle, the complement of the hypotenuse, and the complements of the other angles are called the circular parts of the triangle.

Following Euclid, a right angle is formed by a straight line standing upon another straight line so as to make the adjacent angles equal; any angle less than a right angle is termed an acute angle, and any angle greater than a right angle an obtuse angle.