Elementary Course of Geometry ...Harper & brothers, 1847 - 103 páginas |
Dentro del libro
Resultados 1-5 de 68
Página 13
... and bisects the vertical angle . 3. The perpendicular from the vertex to the base bisects the base and the vertical angle . To prove each of these independently will be an exercise . THEOREM IV . When a triangle has two of its THEOREMS .
... and bisects the vertical angle . 3. The perpendicular from the vertex to the base bisects the base and the vertical angle . To prove each of these independently will be an exercise . THEOREM IV . When a triangle has two of its THEOREMS .
Página 14
... proved that AC can not be greater than AB ; hence AB = AC . Q. E. D. * Corol . Hence every equiangular triangle is ... proving that the negative can not be true , it proves the affirmative . It is also called the reductio ad absurdum ...
... proved that AC can not be greater than AB ; hence AB = AC . Q. E. D. * Corol . Hence every equiangular triangle is ... proving that the negative can not be true , it proves the affirmative . It is also called the reductio ad absurdum ...
Página 20
... prove this it will only be necessary to prove any c two perpendiculars , FH and EG , drawn at random between them , equal . Join A H F G D E B EH . Then the lines FH and EG both being at right angles to AB , will , by the last theorem ...
... prove this it will only be necessary to prove any c two perpendiculars , FH and EG , drawn at random between them , equal . Join A H F G D E B EH . Then the lines FH and EG both being at right angles to AB , will , by the last theorem ...
Página 21
... that line is one of its sides . N.B. - It will be found convenient , when angles have been proved equal , to mark them with the same number of dots as in the figure . THEOREM XV . In any triangle the sum of all THEOREMS . 21.
... that line is one of its sides . N.B. - It will be found convenient , when angles have been proved equal , to mark them with the same number of dots as in the figure . THEOREM XV . In any triangle the sum of all THEOREMS . 21.
Página 29
... and AD must be drawn parallel to the sides AF , BC of the triangles , to complete the parallelograms The above theorem may be proved by th . 1 , and also by th . 5 . ABE is also equal to half the same parallelogram ABCD THEOREMS . 29 12.
... and AD must be drawn parallel to the sides AF , BC of the triangles , to complete the parallelograms The above theorem may be proved by th . 1 , and also by th . 5 . ABE is also equal to half the same parallelogram ABCD THEOREMS . 29 12.
Otras ediciones - Ver todas
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 70 - The areas or spaces of circles are to each other as the squares of their diameters, or of their radii.
Página 50 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.