Elementary Geometry, Plane and Solid: For Use in High Schools and AcademiesMacmillan, 1901 - 440 σελίδες |
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Αποτελέσματα 1 - 5 από τα 100.
Σελίδα vi
... proof in connection with matters which he clearly sees need proving ; other similar problems are inserted where they ... proof , to be sure , but the proofs given in text - books on elementary geometry are as a rule either unsatisfactory ...
... proof in connection with matters which he clearly sees need proving ; other similar problems are inserted where they ... proof , to be sure , but the proofs given in text - books on elementary geometry are as a rule either unsatisfactory ...
Σελίδα vii
... a formal demon- stration . Emphasize the geometric truth presented . Fix as your ideal an elegant , faultless proof , and gradually work up to it . 4. Remember that in this subject the primary object should PREFACE vii.
... a formal demon- stration . Emphasize the geometric truth presented . Fix as your ideal an elegant , faultless proof , and gradually work up to it . 4. Remember that in this subject the primary object should PREFACE vii.
Σελίδα 24
... Proof that the thing constructed is what was required . In the case of a theorem the proof goes to show that the state- ment made in the enunciation is true . 36. In naming a circle we usually mention three points on it , these being ...
... Proof that the thing constructed is what was required . In the case of a theorem the proof goes to show that the state- ment made in the enunciation is true . 36. In naming a circle we usually mention three points on it , these being ...
Σελίδα 25
... these two circles intersect at C. Do these circles necessarily intersect ? If so , at how many points ? Join CA and CB . Then CAB is the triangle required . [ Proof ] Let the pupil make a diagram for 34-37 ] 25 TRIANGLES AND PARALLELOGRAMS.
... these two circles intersect at C. Do these circles necessarily intersect ? If so , at how many points ? Join CA and CB . Then CAB is the triangle required . [ Proof ] Let the pupil make a diagram for 34-37 ] 25 TRIANGLES AND PARALLELOGRAMS.
Σελίδα 26
For Use in High Schools and Academies Thomas Franklin Holgate. [ Proof ] Let the pupil make a diagram for himself and letter it as in the construction . In the triangle CAB , the side AC is a radius of the circle CDF , hence AC equals m ...
For Use in High Schools and Academies Thomas Franklin Holgate. [ Proof ] Let the pupil make a diagram for himself and letter it as in the construction . In the triangle CAB , the side AC is a radius of the circle CDF , hence AC equals m ...
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.