Elements of Plane and Solid GeometryAmerican Book Company, 1903 - 384 σελίδες |
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Σελίδα 9
... line joining any two of its points will lie wholly in the surface . 9. Any combination of points , lines , surfaces , or solids , is a geometrical figure . 10. A figure formed by points and lines in a plane is a plane figure . 11 ...
... line joining any two of its points will lie wholly in the surface . 9. Any combination of points , lines , surfaces , or solids , is a geometrical figure . 10. A figure formed by points and lines in a plane is a plane figure . 11 ...
Σελίδα 13
... line can be drawn joining two points . [ It follows from this axiom that two straight lines can intersect in only one point . ] 14. The shortest distance from one point to another is meas- ured on the straight line joining them . 15 ...
... line can be drawn joining two points . [ It follows from this axiom that two straight lines can intersect in only one point . ] 14. The shortest distance from one point to another is meas- ured on the straight line joining them . 15 ...
Σελίδα 15
... line can be drawn joining two points , AC will coincide with DF . .. the cide throughout and are equal in all respects . coin- Q.E.D. 31. SCHOLIUM . By showing that the A coincide , 15 RECTILINEAR FIGURES.
... line can be drawn joining two points , AC will coincide with DF . .. the cide throughout and are equal in all respects . coin- Q.E.D. 31. SCHOLIUM . By showing that the A coincide , 15 RECTILINEAR FIGURES.
Σελίδα 24
... line . Α ' B Let AB be the given line , and C the given point on the line . Required to erect a perpendicular to AB ... Join F and c . FC is the required perpendicular . For , F and care each equally distant from D and E ( construction ) ...
... line . Α ' B Let AB be the given line , and C the given point on the line . Required to erect a perpendicular to AB ... Join F and c . FC is the required perpendicular . For , F and care each equally distant from D and E ( construction ) ...
Σελίδα 34
... Join B and F. Then will BF bisect ABC . Draw FE and FD . Prove BEF and BDF equal in all respects . Whence ≤1 = ≤ 2 , and Z ABC is bisected . Q.E.F. 95. EXERCISE . At a given point on a line ... line construct an angle equal to 1 R.A.'s . 98 ...
... Join B and F. Then will BF bisect ABC . Draw FE and FD . Prove BEF and BDF equal in all respects . Whence ≤1 = ≤ 2 , and Z ABC is bisected . Q.E.F. 95. EXERCISE . At a given point on a line ... line construct an angle equal to 1 R.A.'s . 98 ...
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Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
AABC AB² ABC and DEF AC² altitude angle formed angles are equal angles equal apothem bisector bisects chord circum circumference cone Construct a triangle COROLLARY cylinder DEFINITION diagonals diameter dihedral angles divided Draw EFGH equally distant equiangular polygon equilateral triangle equivalent EXERCISE exterior angles Find frustum given circle given line given point hypotenuse inscribed angle isosceles triangle joining the middle lateral area Let ABC Let To Prove line joining medians meet middle points number of sides opposite sides parallel parallelogram parallelopiped perimeter perpendicular point of intersection polyhedron prism prolonged PROPOSITION Prove ABCD pyramid quadrilateral radii radius rectangle regular inscribed regular polygon rhombus right angles right-angled triangle SCHOLIUM secants segments Show similar polygons slant height sphere spherical square straight line surface tangent tetrahedron THEOREM trapezoid triangle ABC trihedral unequal vertex vertical angle volume Whence
Δημοφιλή αποσπάσματα
Σελίδα 167 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Σελίδα 139 - A line parallel to one side of a triangle divides the other two sides proportionally.
Σελίδα 187 - Any two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 202 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Σελίδα 180 - In an inscribed quadrilateral, the product of the diagonals is equal to the sum of the products of the opposite sides.
Σελίδα 90 - In the same circle, or in equal circles, equal chords are equally distant from the center; and, conversely, chords equally distant from the center are equal.
Σελίδα 195 - Since similar triangles are to each other as the squares of their homologous sides, ABC : DBE : : AB' : BD3 ; whence BD = AB J ^5| ~ AB A/— ^ — . j A150 f in -f- n The construction of Fig.
Σελίδα 129 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D ; and read, A is to B as C to D.
Σελίδα 15 - If two triangles have two sides and the included angle of one equal respectively to two sides and the included angle of the other, the triangles are equal.
Σελίδα 17 - If two triangles have two angles and the included side of one equal respectively to two angles and the included side of the other, the triangles are congruent.