Report, Volumes 11-20

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Page 53 - The sum of any two face angles of a trihedral angle is greater than the third face angle.
Page 53 - Every section of a circular cone made by a plane parallel to the base is a circle.
Page 13 - If any portion of the fund invested, as provided by the foregoing section, or any portion of the interest thereon, shall, by any action or contingency, be diminished or lost, it shall be replaced by the State to which it belongs...
Page 52 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.
Page 53 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Page 57 - The three perpendiculars from the vertices of a triangle to the opposite sides (produced if necessary) are called the altitudes...
Page 60 - Nam fere de omnibus controversiis publicis privatisque constituunt, et si quod est admissum facinus, si caedes facta, si de hereditate, si de finibus controversia est, idem decernunt, i S praemia poenasque constituunt ; si qui aut privatus aut populus eorum decreto non stetit, sacrifices interdicunt. Haec poena apud eos est gravissima.
Page 53 - In any triangle, the product of two sides is equal to the product of the segments of the third side formed by the bisector of the opposite angle plus the square of the bisector.
Page 58 - Every point in the bisector of an angle is equally distant from the sides of the angle...
Page 33 - THE SHEFFIELD SCIENTIFIC SCHOOL is devoted to instruction and researches in the mathematical, physical, and natural sciences, with reference to the promotion and diffusion of science, and also to the preparation of young men for such pursuits as require special proficiency in these departments of learning.

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