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 páginas |
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Página 12
... wherefore CA , AB , CB are equal to one another ; and the triangle ABC is therefore equilateral , and it is described upon the given straight line AB . PROP . II . PROB . From a given point to draw a straight line equal to a given ...
... wherefore CA , AB , CB are equal to one another ; and the triangle ABC is therefore equilateral , and it is described upon the given straight line AB . PROP . II . PROB . From a given point to draw a straight line equal to a given ...
Página 13
... Wherefore , from the given point A , a straight line AL has been drawn equal to the given straight line BC . PROP . III . PROB . From the greater of two given straight lines to cut off a part equal to the less . Let AB and C be the two ...
... Wherefore , from the given point A , a straight line AL has been drawn equal to the given straight line BC . PROP . III . PROB . From the greater of two given straight lines to cut off a part equal to the less . Let AB and C be the two ...
Página 14
... wherefore also the point C shall coincide with the point F , because AC is equal to DF : But the point B coincides with the point E ; wherefore the base BC shall coincide with the base EF ( cor . def . 3. ) , and shall be equal to it ...
... wherefore also the point C shall coincide with the point F , because AC is equal to DF : But the point B coincides with the point E ; wherefore the base BC shall coincide with the base EF ( cor . def . 3. ) , and shall be equal to it ...
Página 18
... Wherefore , from the given point C , in te given straight line AB , FC has been drawn at right angles to AB . PROP . XII . PROB . To draw a straight line perpendicular to a given straight line , of an unlimited length , from a given ...
... Wherefore , from the given point C , in te given straight line AB , FC has been drawn at right angles to AB . PROP . XII . PROB . To draw a straight line perpendicular to a given straight line , of an unlimited length , from a given ...
Página 22
... wherefore much more is the angle ABC greater than ACB PROP . XIX . THEOR . The greater angle of every triangle is subtended by the greater side , or has the greater side opposite to it . Let ABC be a triangle , of which the angle ABC is ...
... wherefore much more is the angle ABC greater than ACB PROP . XIX . THEOR . The greater angle of every triangle is subtended by the greater side , or has the greater side opposite to it . Let ABC be a triangle , of which the angle ABC is ...
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 12 - AB; but things which are equal to the same are equal to one another...
Página 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.
Página 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.
Página 35 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.