Elementary Geometry, Plane and Solid: For Use in High Schools and AcademiesMacmillan, 1901 - 440 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 92.
Σελίδα 15
... prop- erty or the possibility of constructing some simple figure , we say that we postulate these things . A few of these fundamental assumptions or postulates have already crept into our discussions along with the definitions and ...
... prop- erty or the possibility of constructing some simple figure , we say that we postulate these things . A few of these fundamental assumptions or postulates have already crept into our discussions along with the definitions and ...
Σελίδα 34
... ( Prop . IV . ) Therefore B equals ≤ C , these being corresponding angles , i.e. opposite equal sides , in the two triangles . 49. The proof of this proposition contains the proof of the following theorem : The straight line which ...
... ( Prop . IV . ) Therefore B equals ≤ C , these being corresponding angles , i.e. opposite equal sides , in the two triangles . 49. The proof of this proposition contains the proof of the following theorem : The straight line which ...
Σελίδα 35
... Prop . IV . ) 6. Prove that the triangle whose vertices are the mid - points of the sides of an isosceles triangle is isosceles . ( Apply Prop . IV . ) 7. If on the sides AB , BC , CA , of an equilateral triangle ABC , equal lengths AP ...
... Prop . IV . ) 6. Prove that the triangle whose vertices are the mid - points of the sides of an isosceles triangle is isosceles . ( Apply Prop . IV . ) 7. If on the sides AB , BC , CA , of an equilateral triangle ABC , equal lengths AP ...
Σελίδα 37
... ( Prop . VI . ) Why ? ( Axiom 2. ) But BDC is EDF , which is therefore equal to Z BAC . Hence in As BAC and EDF , two sides and the included angle of one are equal , respectively , to two sides and the in- cluded angle of the other . Name ...
... ( Prop . VI . ) Why ? ( Axiom 2. ) But BDC is EDF , which is therefore equal to Z BAC . Hence in As BAC and EDF , two sides and the included angle of one are equal , respectively , to two sides and the in- cluded angle of the other . Name ...
Σελίδα 38
... ( Prop . II . ) Then AF is the required line . Proof . Compare As ADF and AEF side for side . These triangles are equal in all respects . Where proved ? Therefore DAF equals EAF . That is / BAC is bisected by AF . 55. It should be noticed ...
... ( Prop . II . ) Then AF is the required line . Proof . Compare As ADF and AEF side for side . These triangles are equal in all respects . Where proved ? Therefore DAF equals EAF . That is / BAC is bisected by AF . 55. It should be noticed ...
Άλλες εκδόσεις - Προβολή όλων
Elementary Geometry, Plane and Solid; for Use in High Schools and Academies Thomas F 1859-1945 Holgate Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Elementary Geometry Plane and Solid: For Use in High Schools and Academies Thomas F. Holgate Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD AC² adjacent angles altitude angle formed angles are equal apothem base bisector bisects centre chord coincide convex convex polygon COROLLARY DEFINITION diagonals diameter dicular dihedral angle draw equal angles equal in area equiangular equidistant equilateral triangle EXERCISES face angles figure given circle given line-segment given plane given point given straight line greater Hence hypotenuse identically equal interior angles isosceles triangle length Let ABC line perpendicular magnitudes measure mid-point number of sides opposite sides pair parallel planes parallelepiped parallelogram perimeter perpen plane angles point of contact point of intersection polyhedral angle polyhedron prism Proof Prop Proposition VIII pyramid quadrilateral radii radius ratio rectangle regular polygon required to prove respectively right angles right triangle segments side BC similar sphere square subtended supplementary angle surface tangent tetrahedron theorem triangle ABC triangle is equal trihedral vertex volume
Δημοφιλή αποσπάσματα
Σελίδα 187 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 230 - The formula states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the base and altitude.
Σελίδα 55 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C...
Σελίδα 76 - The line which joins the mid-points of two sides of a triangle is parallel to the third side and equal to one half of it.
Σελίδα 43 - Prove that, if two sides of a triangle are unequal, the angle opposite the greater side is greater than the angle opposite the less.
Σελίδα 231 - A polygon of three sides is called a triangle ; one of four sides, a quadrilateral; one of five sides, a, pentagon; one of six sides, a hexagon ; one of seven sides, a heptagon ; one of eight sides, an octagon ; one of ten sides, a decagon ; one of twelve sides, a dodecagon.
Σελίδα 27 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Σελίδα 200 - The area of a triangle is equal to half the product of its base by its altitude.
Σελίδα 161 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.
Σελίδα 229 - Two parallelograms are similar when they have an angle of the one equal to an angle of the other, and the including sides proportional.