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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Σελίδα 9
... centre of the circle . 13. A diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . 14. A semicircle is the figure contained by a diameter and the part of the circumference cut ...
... centre of the circle . 13. A diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . 14. A semicircle is the figure contained by a diameter and the part of the circumference cut ...
Σελίδα 11
... centre , at any distance from that centre . AXIOMS . 1. THINGS which are equal to the same thing are equal to one another . 2. If equals be added to equals , the wholes are equal . 3. If equals be taken from equals , the remainders are ...
... centre , at any distance from that centre . AXIOMS . 1. THINGS which are equal to the same thing are equal to one another . 2. If equals be added to equals , the wholes are equal . 3. If equals be taken from equals , the remainders are ...
Σελίδα 12
... centre A , at the dis- tance AB , describe ( 3. Postulate ) the circle BCD , and from the cen- tre B , at the distance BA , describe the circle ACE ; and from the point C , in which the circles cut one an- other , draw the straight ...
... centre A , at the dis- tance AB , describe ( 3. Postulate ) the circle BCD , and from the cen- tre B , at the distance BA , describe the circle ACE ; and from the point C , in which the circles cut one an- other , draw the straight ...
Σελίδα 13
... centre A , and at the distance AD , describe ( 3. Post . ) the circle DEF ; and because A is the centre of the circle DEF , AE is equal to AD ; but the straight line C is likewise equal to AD ; A E B whence AE and C are each of them ...
... centre A , and at the distance AD , describe ( 3. Post . ) the circle DEF ; and because A is the centre of the circle DEF , AE is equal to AD ; but the straight line C is likewise equal to AD ; A E B whence AE and C are each of them ...
Σελίδα 18
... centre C , at the distance CD , describe ( 3. Post . ) the circle EGF meeting AB in F , G : and bisect ( 10. 1. ) FG in H , and join CF , CH , CG ; the straight line CH , drawn from the given point C , is per- pendicular to the given ...
... centre C , at the distance CD , describe ( 3. Post . ) the circle EGF meeting AB in F , G : and bisect ( 10. 1. ) FG in H , and join CF , CH , CG ; the straight line CH , drawn from the given point C , is per- pendicular to the given ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angle BCD base BC bisected centre chord circle ABC circumference cosine cylinder 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 produced 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 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 147 - 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 242 - 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 119 - 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...