Elements of Plane and Solid GeometryAmerican Book Company, 1903 - 384 σελίδες |
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Αποτελέσματα 1 - 5 από τα 48.
Σελίδα 79
... radii of the same circle are equal . Arc Chord Diameter Radius A straight line passing through the center and limited by the circumference is a diameter . Every diameter is composed of two radii ; therefore all diam eters of the same ...
... radii of the same circle are equal . Arc Chord Diameter Radius A straight line passing through the center and limited by the circumference is a diameter . Every diameter is composed of two radii ; therefore all diam eters of the same ...
Σελίδα 82
... radii oc and OD . = Apply § 168 to △ OCD , recollecting that AB OC + OD . Q.E.D. 255. EXERCISE . Prove this Proposition ( § 254 ) , using a figure in which the given chord CD intersects the diameter AB . 256. EXERCISE . Through a point ...
... radii oc and OD . = Apply § 168 to △ OCD , recollecting that AB OC + OD . Q.E.D. 255. EXERCISE . Prove this Proposition ( § 254 ) , using a figure in which the given chord CD intersects the diameter AB . 256. EXERCISE . Through a point ...
Σελίδα 83
... radii to the three points . Now we have three equal lines ( why equal ? ) drawn from the point to the line AB , which contradicts ( ? ) . Therefore the supposition that AB could intersect the circum- ference in more than two points is ...
... radii to the three points . Now we have three equal lines ( why equal ? ) drawn from the point to the line AB , which contradicts ( ? ) . Therefore the supposition that AB could intersect the circum- ference in more than two points is ...
Σελίδα 84
... radii . ό C Let the whose centers are O and C have equal radii . To Prove the equal . Proof . Place the O whose center is 0 upon the ○ whose center is C , so that their centers coincide . Then will their circumferences also coincide ...
... radii . ό C Let the whose centers are O and C have equal radii . To Prove the equal . Proof . Place the O whose center is 0 upon the ○ whose center is C , so that their centers coincide . Then will their circumferences also coincide ...
Σελίδα 85
... radii form- ing equal angles at the center intercept equal arcs of the circumference ; and conversely , radii intercepting equal arcs of the circumference form equal angles at the center . Q Q Let ABC and DEF be two equal angles at the ...
... radii form- ing equal angles at the center intercept equal arcs of the circumference ; and conversely , radii intercepting equal arcs of the circumference form equal angles at the center . Q Q Let ABC and DEF be two equal angles at the ...
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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.