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 sider |
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Resultat 1-5 av 39
Side 32
... consequently , the op- posite sides are parallel ; namely , the side AB parallel to CD , and BD pa- rallel to AC ; and , therefore , the figure is a parallelogram . COR . 3. Hence , also , if the opposite angles of a quadrilateral be ...
... consequently , the op- posite sides are parallel ; namely , the side AB parallel to CD , and BD pa- rallel to AC ; and , therefore , the figure is a parallelogram . COR . 3. Hence , also , if the opposite angles of a quadrilateral be ...
Side 42
... consequently , the angle ACD is greater than the angle ADC ; and , since the greater side is opposite to the greater angle ( 19. 1. ) ; therefore the side AD is greater than the side AC . COR . 1. The perpendicular measures the true ...
... consequently , the angle ACD is greater than the angle ADC ; and , since the greater side is opposite to the greater angle ( 19. 1. ) ; therefore the side AD is greater than the side AC . COR . 1. The perpendicular measures the true ...
Side 43
... consequently AH = DF . Now ( by hyp . ) , we have DF AC ; and therefore , AH AC . But by the last prop- osition , the oblique line AC can- not be equal to the oblique line AH , which lies nearer to the per- pendicular AB ; therefore it ...
... consequently AH = DF . Now ( by hyp . ) , we have DF AC ; and therefore , AH AC . But by the last prop- osition , the oblique line AC can- not be equal to the oblique line AH , which lies nearer to the per- pendicular AB ; therefore it ...
Side 86
... consequently divides the circle into two equal parts ; hence the portion AEF is equal to the portion AEFB , which is absurd . COR . The arc of a circle whose chord is a diameter , is a semicircum- ference , and the included segment is a ...
... consequently divides the circle into two equal parts ; hence the portion AEF is equal to the portion AEFB , which is absurd . COR . The arc of a circle whose chord is a diameter , is a semicircum- ference , and the included segment is a ...
Side 87
... consequently lie in the circumference of the circle , whose centre is F , and radius FA . It is obvious , that besides this , no other circumference can pass through the same points ; for the centre , lying in the perpen- A B E ༧ ...
... consequently lie in the circumference of the circle , whose centre is F , and radius FA . It is obvious , that besides this , no other circumference can pass through the same points ; for the centre , lying in the perpen- A B E ༧ ...
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Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 12 - AB; but things which are equal to the same are equal to one another...
Side 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.
Side 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.
Side 35 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.