## Selected Propositions in Geometrical Constructions and Applications of Algebra to Geometry: Being a Key to the Appendix of Davies' Legendre. (With a Supplement). |

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SEL PROPOSITIONS IN GEOMETRICA Charles 1798-1876 Davies,A. M. (Adrien Marie) 1752-183 Legendre No preview available - 2016 |

Selected Propositions in Geometrical Constructions and Applications of ... Charles Davies,A. M. Legendre No preview available - 2017 |

### Common terms and phrases

ABČ ABCD altitude angles is equal apothem bisectrix chord circumference circumscribed cone consequently construct convex surface cubic feet decagon DEMONSTRATION.-Let ABC denote diagonals diameter dicular diedral angle draw equation equilateral triangle find the area frustum given angle given circle given line given point given triangle hence hypothenuse inscribed circle isosceles triangle Let ABC lines drawn middle point one-half parallel parallelogram pass a plane pendicular pentagon perimeter perpen perpendicular plane PQ point of intersection polygon Prob prolong PROP proved quadrilateral regular inscribed right angle right-angled triangle semiperimeter similar triangles slant height SOLUTION.-Let sphere spherical angles spherical excess spherical pyramid square feet tangent triangle ABC triangle is equal trirectangular triangle vertex vertical angle whence

### Popular passages

Page 56 - IN a Triangle, having given the Base, the Sum of the other two Sides, and the Length of a Line drawn from the Vertical Angle to the Middle of the Base ; to find the Sides of the Triangle.

Page 62 - PROBLEM XVII. IN a Right-angled Triangle, having given the Perimeter or Sum of all the Sides, and the Perpendicular let fall from the Right Angle on the Hypothenuse ; to determine the Triangle, that is, its Sides. PROBLEM XVIII.

Page 10 - The sum of the perpendiculars dropped from any point in the base of an isosceles triangle to the arms, is equal to the altitude upon one of the arms.

Page 69 - To determine a Triangle ; having given the Lengths of three Lines drawn from the three Angles, to the Middle of the opposite Sides.

Page 59 - To determine a Triangle ; having given the Base, the Pe,rpendicular, and the Difference of the two other Sides.

Page 76 - The sum of the interior angles of a polygon is equal to two right angles, taken as many times less two as the figure has sides.

Page 59 - Add together all the 1st determinants formed from the first « arrays, and multiply the sum by the corresponding sum for the second s arrays ; obtain the like product involving all the 2nd determinants, the like product involving all the 3rd determinants, and so on. Then, the sum of these products is equal to the sum of the products obtained by multiplying each array of the first set by each array of the (second set Or we may put it alternatively as a formal proposition, thus : — If a rectangular...

Page 42 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.

Page 94 - The sum of the perpendiculars from any point within an equilateral triangle to the three sides is equal to the altitude of the triangle (Fig.

Page 133 - Prove that if a line is parallel to one plane and perpendicular to another, the two planes are perpendicular to each other.