Elementary Course of Geometry ...Harper & brothers, 1847 - 103 Seiten |
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Seite v
... manner of some of the latest and best French and German treatises . This arrangement , though in the main preserved , has been occasionally departed from , for the sake of rendering a knowledge of the whole subject most easy of ac ...
... manner of some of the latest and best French and German treatises . This arrangement , though in the main preserved , has been occasionally departed from , for the sake of rendering a knowledge of the whole subject most easy of ac ...
Seite 10
... manner analogous to the corresponding opera- tion in Arithmetic and Algebra , by applying the smaller line to the larger as many times as it will go ; and the remainder to the smaller given line , and so on . This may be done by taking ...
... manner analogous to the corresponding opera- tion in Arithmetic and Algebra , by applying the smaller line to the larger as many times as it will go ; and the remainder to the smaller given line , and so on . This may be done by taking ...
Seite 11
... manner that the point A may coincide with the point D , and the side AB with the side DE , which is equal to it . Then , since the angle A is equal to the angle D ( by hyp . ) , † the side AC must differ in direction from the side AB by ...
... manner that the point A may coincide with the point D , and the side AB with the side DE , which is equal to it . Then , since the angle A is equal to the angle D ( by hyp . ) , † the side AC must differ in direction from the side AB by ...
Seite 12
... manner that the side AB may fall exactly on the equal side DE . Then , since the angle A is equal to the angle D ( by hyp . ) , the side AC must fall on the side DF ; and , in like man- ner , because the angle B is equal to the angle E ...
... manner that the side AB may fall exactly on the equal side DE . Then , since the angle A is equal to the angle D ( by hyp . ) , the side AC must fall on the side DF ; and , in like man- ner , because the angle B is equal to the angle E ...
Seite 14
... manner it might be proved that AC can not be greater than AB ; hence AB = AC . Q. E. D. * Corol . Hence every equiangular triangle is also equilateral . THEOREM V. When two triangles have all the three sides in the one equal to all the ...
... manner it might be proved that AC can not be greater than AB ; hence AB = AC . Q. E. D. * Corol . Hence every equiangular triangle is also equilateral . THEOREM V. When two triangles have all the three sides in the one equal to all the ...
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Häufige Begriffe und Wortgruppen
ABCD altitude angles equal axis bisect center of similitude chord circumference cone consequently construct cylinder diagonal diameter dicular divided draw equal angles equal bases equal distances equiangular equilateral triangle figure find a point find the area frustum geometric locus given angle given circle given line given point given triangle gles Hence hypothenuse indeterminate problems inscribed intersection isosceles isosceles triangle Let ABC line drawn line joining locus which resolves measured meet parallel planes parallelogram pendicular pentagon perimeter perpen perpendicular plane angles plane XZ polygon polyhedral angle polyhedrons prism Prob Prop proportional Prove pyramid radical axis radii radius ratio rectangle regular polygon regular polyhedrons resolves this problem rhombus right line right-angled triangle Scholium segment semicircle side AC similar Solution sphere spherical polygon spherical triangle straight line surface symmetric tangent tetrahedrons triangle ABC trihedral angles vertex
Beliebte Passagen
Seite 33 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle.
Seite 70 - The areas or spaces of circles are to each other as the squares of their diameters, or of their radii.
Seite 50 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Seite 50 - Four quantities are said to be proportional when the ratio of the first to the second is the same as the ratio of the third to the fourth.
Seite 60 - Carol. 4. Parallelograms, or triangles, having an angle in each equal, are in proportion to each other as the rectangles of the sides which are about these equal angles. THEOREM LXXXII. IF a line be drawn in a triangle parallel to one of its sides, it will cut the other two sides proportionally.
Seite 23 - 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.
Seite 1 - A straight line is said to be perpendicular to a plane when it is perpendicular to every straight line which passes through its foot in that plane, and the plane is said to be perpendicular to the line.
Seite 51 - Proportion, when the ratio is the same between every two adjacent terms, viz. when the first is to the second, as the second to the third, as the third to the fourth, as the fourth to the fifth, and so on, all in the same common ratio.
Seite 5 - ... 07958 in using the circumferences j then taking one-third of the product, to multiply by the length, for the content. Ex. 1. To find the number of solid feet in a piece of timber, whose bases are squares, each side of the greater end being 15 inches, and each side of the less end 6 inches ; also, the length or perpendicular altitude 2-1 feet.
Seite 2 - What is the upright surface of a triangular pyramid, the slant height being 20 feet, and each side of the base 3 feet ? • Ans.