Elements of geometry, containing the first two (third and fourth) books of Euclid, with exercises and notes, by J.H. Smith, Parte 1

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Sommario

 Sezione 1 1 Sezione 2 3 Sezione 3 10 Sezione 4 13 Sezione 5 16 Sezione 6 21 Sezione 7 25 Sezione 8 36
 Sezione 11 44 Sezione 12 52 Sezione 13 61 Sezione 14 70 Sezione 15 71 Sezione 16 76 Sezione 17 78 Sezione 18 91

 Sezione 9 37 Sezione 10 42
 Sezione 19 92

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Pagina 52 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Pagina 69 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Pagina 83 - If a straight line be bisected, and produced to any point; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced.
Pagina 17 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Pagina 48 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles...
Pagina 26 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Pagina 86 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Pagina 90 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side...
Pagina 106 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC.
Pagina 82 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.