Elements of Geometry: Containing the First Six Books of Euclid with a Supplement on the Quadrature of the Circle, and the Geometry of Solids : to which are Added, Elements of Plane and Spherical TrigonometryJ.P. Lippincott & Company, 1856 - 318 σελίδες |
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Αποτελέσματα 1 - 5 από τα 98.
Σελίδα 6
... perpendicular to another ; or to divide a line into two equal parts . 9. Solution of a problem is the resolution or answer given to it . A Numerical or Numeral solution , is the answer given in numbers . A Geometrical solution , is the ...
... perpendicular to another ; or to divide a line into two equal parts . 9. Solution of a problem is the resolution or answer given to it . A Numerical or Numeral solution , is the answer given in numbers . A Geometrical solution , is the ...
Σελίδα 18
... perpendicular to a given straight line , of an unlimited length , from a given point without it . Let AB be a given straight line , which may be produced to any length both ways , and let C be a point without it . It is required to draw ...
... perpendicular to a given straight line , of an unlimited length , from a given point without it . Let AB be a given straight line , which may be produced to any length both ways , and let C be a point without it . It is required to draw ...
Σελίδα 28
... perpendicular to a third line , they will be parallel to each other . PROP . XXIX . THEOR . 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 ...
... perpendicular to a third line , they will be parallel to each other . PROP . XXIX . THEOR . 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 ...
Σελίδα 29
... perpendicular to one of two parallels , is perpendicular to the other . COR . 3. Since AGE = BGH , and DHF = CHG ; hence the four acute angles BGH , AGE , GHC , DHF , are equal to each other . The same is the case with the four obtuse ...
... perpendicular to one of two parallels , is perpendicular to the other . COR . 3. Since AGE = BGH , and DHF = CHG ; hence the four acute angles BGH , AGE , GHC , DHF , are equal to each other . The same is the case with the four obtuse ...
Σελίδα 41
... base BC , the angle DAC is equal ( 8. 1. ) to the angle BAC ; But DAC is a right angle ; therefore also BAC is a right angle . ADDITIONAL PROPOSITIONS . PROP . A. THEOR . A perpendicular 6 OF GEOMETRY . BOOK I. 41 H ...
... base BC , the angle DAC is equal ( 8. 1. ) to the angle BAC ; But DAC is a right angle ; therefore also BAC is a right angle . ADDITIONAL PROPOSITIONS . PROP . A. THEOR . A perpendicular 6 OF GEOMETRY . BOOK I. 41 H ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder definition demonstrated described diameter divided draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional proposition radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line AC tangent THEOR third touches the circle triangle ABC triangle DEF wherefore
Δημοφιλή αποσπάσματα
Σελίδα 51 - 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.
Σελίδα 81 - IF a straight line touch a circle, and from the point of contact a straight line be drawn at right angles to the touching line, the centre of the circle shall be in that line.
Σελίδα 14 - The angles at the base of an Isosceles triangle are equal to one another ; and if the equal sides be produced, the angles upon the other side of the base shall be equal.
Σελίδα 19 - The angles which one straight line makes with another upon one side uf it, are, either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it the angles CBA, ABD ; these are either two right angles, or are together equal to two right angles. For, if the angle CBA be equal to ABD, each of them is a right angle (Def.
Σελίδα 52 - If a straight line be divided into any two parts, the squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square on the other part. Let the straight line AB be divided into any two parts in the point C. Then the squares on AB, BC shall be equal to twice the rectangle AB, BC, together with the square on A C.
Σελίδα 149 - If the vertical angle of a triangle be bisected by a straight line which also cute the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Σελίδα 244 - 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.
Σελίδα 9 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Σελίδα 121 - Reciprocal figures, viz. triangles and parallelograms, " are such as have their sides about two of their " angles proportionals in such a manner, that a side
Σελίδα 72 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...