Elements of geometry, containing the first two (third and fourth) books of Euclid, with exercises and notes, by J.H. Smith, Del 11871 |
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Side 33
... difference between the other two sides . Ex . 3. Prove that the sum of the distances of any point from the angular points of a quadrilateral is greater than half the perimeter of the quadrilateral . Ex . 4. If one side of a triangle be ...
... difference between the other two sides . Ex . 3. Prove that the sum of the distances of any point from the angular points of a quadrilateral is greater than half the perimeter of the quadrilateral . Ex . 4. If one side of a triangle be ...
Side 41
... difference between MB and MN is less than that between AB and AN . 2. ABC is a triangle , and the angle at A is bisected by a straight line which meets BC at D : shew that BA is greater than BD , and CA greater than CD . 3. AB , AC are ...
... difference between MB and MN is less than that between AB and AN . 2. ABC is a triangle , and the angle at A is bisected by a straight line which meets BC at D : shew that BA is greater than BD , and CA greater than CD . 3. AB , AC are ...
Side 56
... difference between the angles at B and C. 6. If the straight line AD bisect the angle at A of the triangle ABC , and BDE be drawn perpendicular to AD , and meeting AC , or AC produced , in E ; shew that BD is equal to DE . 7. Divide a ...
... difference between the angles at B and C. 6. If the straight line AD bisect the angle at A of the triangle ABC , and BDE be drawn perpendicular to AD , and meeting AC , or AC produced , in E ; shew that BD is equal to DE . 7. Divide a ...
Side 67
... difference of the triangles thus formed is equal to half the parallelogram . Ex . 2. The two triangles , formed by drawing straight lines from any point within a parallelogram to the extremities of its opposite sides , are together half ...
... difference of the triangles thus formed is equal to half the parallelogram . Ex . 2. The two triangles , formed by drawing straight lines from any point within a parallelogram to the extremities of its opposite sides , are together half ...
Side 75
... difference between the squares on the sides is equal to the difference between the squares on the segments of the base . PROPOSITION XLVIII . THEOREM . If the square described upon BOOK I. PROP . XLVII . 75.
... difference between the squares on the sides is equal to the difference between the squares on the segments of the base . PROPOSITION XLVIII . THEOREM . If the square described upon BOOK I. PROP . XLVII . 75.
Andre utgaver - Vis alle
Elements of Geometry, Containing the First Two (Third and Fourth) Books of ... Euclides Ingen forhåndsvisning tilgjengelig - 2016 |
Elements of Geometry, Containing the First Two (Third and Fourth) Books of ... Euclides Ingen forhåndsvisning tilgjengelig - 2018 |
Elements of Geometry, Containing the First Two (Third and Fourth) Books of ... Euclides Ingen forhåndsvisning tilgjengelig - 2015 |
Vanlige uttrykk og setninger
AB=DE ABCD acute adjacent alternate angles equal angular points applied base bisected Book called centre circle coincide common construction describe diagonal difference distance divided double draw equal equidistant Euclid Exercises extremities fall figure four Geometry given point given straight line greater half Hence interior angles intersect isosceles triangle join length less Let ABC line joining magnitude measure meet method NOTE obtuse opposite sides parallel parallelogram perpendicular placed polygon position Post Postulate PROBLEM produced proof Prop PROPOSITION proved Q. E. D. Ex quadrilateral rectangle contained respects right angles Shew shewn sides square sum of sqq suppose Surface Take taken THEOREM triangle ABC triangles are equal unequal vertex vertical whole
Populære avsnitt
Side 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.
Side 69 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Side 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.
Side 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.
Side 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...
Side 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.
Side 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.
Side 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...
Side 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.
Side 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.