The Melbourne University Calendar

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University., 1909

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Página 343 - If two circles touch, the point of contact lies on the straight line through the centres. The angle which an arc of a circle subtends at the centre is double that which it subtends at any point on the remaining part of the circumference. Angles in the same segment of a circle are equal...
Página 342 - The square on a side of a triangle is greater than, equal to, or less than, the sum of the squares on the other two sides, according as the angle contained by those sides is obtuse, right or acute. The difference in the...
Página 342 - In equal circles (or, in the same circle) (i) if two arcs subtend equal angles at the centres, they are equal; (ii) conversely, if two arcs are equal, they subtend equal angles at the centres. In equal circles (or, in the same circle) (i) if two chords are equal, they cut off equal arcs ; (ii) conversely, if two arcs are equal, the chords of the arcs are equal.
Página 336 - When a straight line cuts two other straight lines, if (i) a pair of alternate angles are equal, or ii) a pair of corresponding angles are equal, or (iii) a pair of interior angles on the same side of the cutting line are together equal to two right angles, then the two straight lines are parallel ; and the converse. Straight lines which are parallel to the same straight line are parallel to one another.
Página 337 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Página 336 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Página xxxvii - Senate by the majority of the members present ; and the chairman at any such meeting shall have a vote, and, in case of an equality of votes, a second or casting vote.
Página 336 - ANGLES AT A POINT. If a straight line stands on another straight line, the sum of the two angles so formed is equal to two right angles ; and the converse.
Página 337 - If two right-angled triangles have their hypotenuses equal, and one side of the one equal to one side of the other, the triangles are congruent. If two sides of a triangle are unequal, the greater side has the greater angle opposite to it ; and the converse. Of all the straight lines that can be drawn to a given straight line from a given point outside it, the perpendicular is the shortest.
Página 374 - If a straight line is perpendicular to each of two intersecting straight lines at their point of intersection, it is also perpendicular to the plane in which they lie.

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