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, 1849 - 317 páginas |
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Página 61
... chord or subtense of an arc is the straight line which joins its two ex- tremities . C. A straight line is said to be inscribed in a circle , when the extremities of it are in the circumference of the circle . And any straight line ...
... chord or subtense of an arc is the straight line which joins its two ex- tremities . C. A straight line is said to be inscribed in a circle , when the extremities of it are in the circumference of the circle . And any straight line ...
Página 62
... chords or arcs which their sides include . 8. The sector of a circle is the figure contained by two straight lines drawn from the centre , and the arc of the circumference between them . 9. Similar segments of a circle , are those in ...
... chords or arcs which their sides include . 8. The sector of a circle is the figure contained by two straight lines drawn from the centre , and the arc of the circumference between them . 9. Similar segments of a circle , are those in ...
Página 64
... chord , passes through the centre ; for this perpendicular is the same as the one let fall from the centre on the same chord , since both of them passes through the middle of the chord . COR . 2. It likewise follows , that the ...
... chord , passes through the centre ; for this perpendicular is the same as the one let fall from the centre on the same chord , since both of them passes through the middle of the chord . COR . 2. It likewise follows , that the ...
Página 71
... chord is , the farther it is from the centre ; and , conversely , the farther the chord is from the centre , the shorter it is . PROP . XVI . THEOR . The straight line drawn at right angles to the diameter of a circle , from the ...
... chord is , the farther it is from the centre ; and , conversely , the farther the chord is from the centre , the shorter it is . PROP . XVI . THEOR . The straight line drawn at right angles to the diameter of a circle , from the ...
Página 86
... chord is a diameter , is a semicircum- ference , and the included segment is a semicircle . PROP . B. THEOR . Through three given points which are not in the same straight line , one cir- cumference of a circle may be made to pass , and ...
... chord is a diameter , is a semicircum- ference , and the included segment is a semicircle . PROP . B. THEOR . Through three given points which are not in the same straight line , one cir- cumference of a circle may be made to pass , and ...
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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 definition 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 solid parallelopiped spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore
Pasajes populares
Página 149 - 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.
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 on the line between the points of section, is equal to the square on half the line.
Página 29 - Straight lines which are parallel to the same straight line are parallel to one another. Triangles and Rectilinear Figures. The sum of the angles of a triangle is equal to two right angles.
Página 52 - If a straight line be bisected, and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Página 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.
Página 296 - 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 15 - UPON the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.
Página 283 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...
Página 22 - Any two sides of a triangle are together greater than the third side.
Página 26 - ... sides be equal, each to each; and also the third angle of the one to the third angle of the other. Let ABC, DEF be two triangles which have the angles ABC, BCA equal to the angles DEF, EFD, viz.