Scientific and practical geometry for self-instruction1879 |
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Page xi
... Euclid , including the doctrine of " Obliques " and the comparative lengths of " Chords in Circles ; " attaining results by a single tool where many are used in Euclid . The remaining Sections of Div . C ( 28 to INTRODUCTION . xi.
... Euclid , including the doctrine of " Obliques " and the comparative lengths of " Chords in Circles ; " attaining results by a single tool where many are used in Euclid . The remaining Sections of Div . C ( 28 to INTRODUCTION . xi.
Page 7
... Chord , a right line connecting the two extremes of an arc ( P p ) . Segment , any part of a circle bounded by an arc and chord ( P p P ) . Semicircle , a segment of which the chord passes through the centre , and is thus a diameter ...
... Chord , a right line connecting the two extremes of an arc ( P p ) . Segment , any part of a circle bounded by an arc and chord ( P p P ) . Semicircle , a segment of which the chord passes through the centre , and is thus a diameter ...
Page 8
... chords and their intercepted arcs ( sljPs ) . Concentric Circles have the same centres but different lengths of radii ... chord being in this case sl , diameter ) . Tangent to a circle or any other curve is a right line which touches it ...
... chords and their intercepted arcs ( sljPs ) . Concentric Circles have the same centres but different lengths of radii ... chord being in this case sl , diameter ) . Tangent to a circle or any other curve is a right line which touches it ...
Page 26
... CHORD OR AN ARC ( Fig . B 14 ) . Let ab mark the chord and acb the arc . By Sect . 15 bisect the chord ( at d ) , and through d ( Sect . 12 ) draw the perpendicular xy in both directions , and it will bisect the arc ( C , Sect . 37 ) ...
... CHORD OR AN ARC ( Fig . B 14 ) . Let ab mark the chord and acb the arc . By Sect . 15 bisect the chord ( at d ) , and through d ( Sect . 12 ) draw the perpendicular xy in both directions , and it will bisect the arc ( C , Sect . 37 ) ...
Page 38
... chords of which the arcs will together exactly include the circumference . IRREGULAR FIGURES are those in which the sides are not equal and admit of almost endless variety , and in general they would not exactly include the ...
... chords of which the arcs will together exactly include the circumference . IRREGULAR FIGURES are those in which the sides are not equal and admit of almost endless variety , and in general they would not exactly include the ...
Common terms and phrases
ab² abcd ac² adjacent angles altitude angles equal angles Sect Application axis bisected centre chord circle circumference consequently construction continued contour corresponding angles cutting deduction demonstration diagonal diameter distance divided division draw arc draw line draw the indefinite drawn ellipse equal angles equal bases equal Sect equal sides equidistant equivalent triangle Euclid example exterior angle external angle four right angles frustrum geometrical operations give greater hypothenuse inches included angle indefinite line isosceles triangle length Let abc let fall line ac line cd mark measure half mode Multiply number of sides oblique opposed angle parallel ruler parallelogram pendicular polygons proof proposition radii ratio rectangle reflex angle rhombus right line rule in Sect secant Sectns segment semicircle set square side ab side ac similar triangles slant height summit supplementary angles tangent third side trapezium triangle abc
Popular passages
Page 14 - 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...
Page 8 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Page 7 - A circle is a plane figure bounded by a curved line called the circumference, every point of which is equally distant from a point within called the center, Fig.
Page 96 - Any two sides of a triangle are together greater than the third side.
Page 73 - Parallelograms on the same base, and between the same parallels, are equal to one another.
Page 278 - Therefore all the interior angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 14 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.
Page 266 - A sphere is a solid, bounded by a curved surface, every part of which is equally distant from a point within, called the centre.
Page 45 - From a given point without a line, to draw a perpendicular to that line. Let AB be the given line, and C the given point. From C draw any oblique line, as Cn.
Page 9 - The sign, + , which is read plus, indicates that the numbers between which it is placed are to be added ; thus, 6 + 4, means, that 4 is to be added to 6.