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, 1846 - 317 σελίδες |
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Αποτελέσματα 1 - 5 από τα 67.
Σελίδα 12
... fore CA is equal to CB ; 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 ...
... fore CA is equal to CB ; 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 ...
Σελίδα 17
... fore the given rectilineal angle BAC is bisect- ed by the straight line AF . SCHOLIUM . B D F E By the same construction , each of the halves BAF , CAF , may be divi- ded into two equal parts ; and thus , by successive subdivisions , a ...
... fore the given rectilineal angle BAC is bisect- ed by the straight line AF . SCHOLIUM . B D F E By the same construction , each of the halves BAF , CAF , may be divi- ded into two equal parts ; and thus , by successive subdivisions , a ...
Σελίδα 30
... fore also the angles CBA , BAC , ACB are equal to two right angles . D COR . 1. All the interior angles of any rectilineal figure are equal to twice as many right angles as the figure has sides , wanting four right angles . For any ...
... fore also the angles CBA , BAC , ACB are equal to two right angles . D COR . 1. All the interior angles of any rectilineal figure are equal to twice as many right angles as the figure has sides , wanting four right angles . For any ...
Σελίδα 33
... fore the opposite sides and angles of a parallelogram are equal to one an- other ; also , its diameter bisects it ; for AB being equal to CD , and BC common , the two AB , BC are equal to the two DC , CB , each to each ; now the angle ...
... fore the opposite sides and angles of a parallelogram are equal to one an- other ; also , its diameter bisects it ; for AB being equal to CD , and BC common , the two AB , BC are equal to the two DC , CB , each to each ; now the angle ...
Σελίδα 35
... fore , each of the figures EBCA , DBCF is a parallelogram ; and EBCA E B A D C F is equal ( 35. 1. ) to DBCF , because they are upon the same base BC , and between the same parallels BC , EF ; but the triangle ABC is the half of the ...
... fore , each of the figures EBCA , DBCF is a parallelogram ; and EBCA E B A D C F is equal ( 35. 1. ) to DBCF , because they are upon the same base BC , and between the same parallels BC , EF ; but the triangle ABC is the half of the ...
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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 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 magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular plane 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 solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore
Δημοφιλή αποσπάσματα
Σελίδα 49 - 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 147 - ... cuts 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 292 - 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 7 - 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 139 - K hag to M the ratio which is compounded of the ratios of the sides ; therefore also the parallelogram AC has to the parallelogram CF the ratio which is compounded of the ratios of the sides. COR. Hence, any two rectangles are to each other as the products of their bases multiplied by their altitudes.
Σελίδα 33 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Σελίδα 79 - 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...
Σελίδα 125 - 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 131 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means; And if the rectangle contained by the extremes be equal to the rectangle contained by the means, the four straight lines are proportionals. Let the four straight lines, AB, CD, E, F, be proportionals, viz.
Σελίδα 78 - 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.