Elements of plane (solid) geometry (Higher geometry) and trigonometry (and mensuration), being the first (-fourth) part of a series on elementary and higher geometry, trigonometry, and mensuration |
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Seite 5
... similar triangles , at once elegant and satisfactory , and to deduce directly from this , in the most conclusive manner , the general property that similar triangles and polygons are proportional to the squares on their homologous sides ...
... similar triangles , at once elegant and satisfactory , and to deduce directly from this , in the most conclusive manner , the general property that similar triangles and polygons are proportional to the squares on their homologous sides ...
Seite 75
... similar , and similar to those of the former triangle . PROPOSITION XXIV . THEOREM . If from any point of the base of a right angled triangle , as a centre , or from any point of the base produced opposite the right angle as a centre ...
... similar , and similar to those of the former triangle . PROPOSITION XXIV . THEOREM . If from any point of the base of a right angled triangle , as a centre , or from any point of the base produced opposite the right angle as a centre ...
Seite 86
... Similar figures are those which have their angles re- spectively equal each to each , and their homologous sides . proportional . 2. In two different circles , similar arcs , sectors or segments , are those which correspond to equal ...
... Similar figures are those which have their angles re- spectively equal each to each , and their homologous sides . proportional . 2. In two different circles , similar arcs , sectors or segments , are those which correspond to equal ...
Seite 99
... similar when they have their angles equal , each to each , and their homologous sides proportional ( Def . 1. ) ; consequently the equiangular triangles BAC , CED , are two similar figures . Scholium . Observe , that in similar ...
... similar when they have their angles equal , each to each , and their homologous sides proportional ( Def . 1. ) ; consequently the equiangular triangles BAC , CED , are two similar figures . Scholium . Observe , that in similar ...
Seite 100
... similar triangles are proportional , the sum of their sides or their perimeters are proportional also as their homologous sides . PROPOSITION XVIII . THEOREM . Conversely , two triangles , which have their homologous sides proportional ...
... similar triangles are proportional , the sum of their sides or their perimeters are proportional also as their homologous sides . PROPOSITION XVIII . THEOREM . Conversely , two triangles , which have their homologous sides proportional ...
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Elements of Plane (Solid) Geometry (Higher Geometry) and Trigonometry (and ... Nathan Scholfield Keine Leseprobe verfügbar - 2015 |
Häufige Begriffe und Wortgruppen
ABCD abscissa altitude axis bisect chord circle circular segment circum circumference circumscribing cone conjugate construction convex surface cosec cosine cube curve cylinder described diameter distance divided draw ellipse equal to half equation equivalent feet figure formed frustum Geom geometry given hence hyperbola hypothenuse inches inscribed inscribed sphere latus rectum length logarithm magnitude measured multiplied by one-third number of sides opposite ordinates parabola parallel parallelogram perimeter perpendicular plane polyedroid polyedron polygon portion prism PROBLEM Prop proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon revoloid rhomboid right angled triangle right line root Scholium sector segment similar similar triangles sine slant height solid angle sphere spherical square straight line tangent THEOREM triangle ABC triangular triangular prism ungula vertex vertical virtual centre
Beliebte Passagen
Seite 36 - Prove that parallelograms on the same base and between the same parallels are equal in area.
Seite 116 - E to A, from A to B, from B to C, and from C to...
Seite 35 - The sum of any two sides of a triangle, is greater than the third side.
Seite 60 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Seite 56 - In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs.
Seite 38 - The volumes of similar solids are to each other as the cubes of their like dimensions.
Seite 75 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Seite 86 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let...
Seite 211 - To find the solidity of a hyperbolic conoid, or otherwise called a hyperboloid. RULE. To the square of the radius of the base, add the square of the diameter...
Seite 48 - Hence, the interior angles plus four right angles, is equal to twice as many right angles as the polygon has sides, and consequently, equal to the sum of the interior angles plus the exterior angles.