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 TrigonometryW.E. Dean, 1837 - 318 σελίδες |
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Σελίδα 44
... radius equal to AB , the other given side , would cut BC on opposite sides of C ' ; so that only one obtuse angled triangle could be formed ; that is , the triangle BC'A will be the triangle required . B C C And , if the given angle ...
... radius equal to AB , the other given side , would cut BC on opposite sides of C ' ; so that only one obtuse angled triangle could be formed ; that is , the triangle BC'A will be the triangle required . B C C And , if the given angle ...
Σελίδα 45
... radius equal to the other given side , describe an arc , cutting CB in B ; draw AB , and CAB will be the triangle requi- red . But if the given angle is acute , and the side opposite to it less than the other given side ; make the angle ...
... radius equal to the other given side , describe an arc , cutting CB in B ; draw AB , and CAB will be the triangle requi- red . But if the given angle is acute , and the side opposite to it less than the other given side ; make the angle ...
Σελίδα 46
... radius equal to the side of the other square , describe an arc cutting AD in D : the square described upon AD will be equivalent to the difference of the squares constructed upon AC and CD . For the triangle DAC is right angled ...
... radius equal to the side of the other square , describe an arc cutting AD in D : the square described upon AD will be equivalent to the difference of the squares constructed upon AC and CD . For the triangle DAC is right angled ...
Σελίδα 61
... radius of a circle is the straight line drawn from the centre to the circumference . 1. A straight line is said to touch a circle , when it meets the cir- cle , and being produced does not cut it . And that line which has but one point ...
... radius of a circle is the straight line drawn from the centre to the circumference . 1. A straight line is said to touch a circle , when it meets the cir- cle , and being produced does not cut it . And that line which has but one point ...
Σελίδα 85
... radius drawn to the point of contact is perpendicular to the tangent , it follows that the angle included by two tangents , drawn from the same point , is bisected by a line drawn from the centre of the circle to that point ;. for. this.
... radius drawn to the point of contact is perpendicular to the tangent , it follows that the angle included by two tangents , drawn from the same point , is bisected by a line drawn from the centre of the circle to that point ;. for. this.
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar 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 magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle spherical angle spherical triangle square straight line BC 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 12 - AB; but things which are equal to the same are equal to one another...
Σελίδα 80 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Σελίδα 288 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 35 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Σελίδα 81 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles made by this line with the line which touches the circle, shall be equal to the angles in the alternate segments of the circle.
Σελίδα 52 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.
Σελίδα 127 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 23 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle.
Σελίδα 19 - The angles which one straight line makes with another upon one side of 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.