The Elements of Plane and Solid Geometry: With Chapters on Mensuration and Modern GeometryPorter & Coates, 1879 - 266 σελίδες |
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Σελίδα 202
... that AC < AD + DC , and so Hence , AB is less than the sum of AD , DC , etc .; and if these points be taken near enough each other , their sum Proposition 8 . Theorem . - Symmetrical triangles are equal 202 GEOMETRY - BOOK IX .
... that AC < AD + DC , and so Hence , AB is less than the sum of AD , DC , etc .; and if these points be taken near enough each other , their sum Proposition 8 . Theorem . - Symmetrical triangles are equal 202 GEOMETRY - BOOK IX .
Σελίδα 203
... symmetrical triangles are respectively equal . Let ABC be a spherical triangle ; produce the radii through its angles beyond the centre to meet the sphere in A'B'C ' ; then the sides and angles of ABC , A'B'C ' are respectively equal ...
... symmetrical triangles are respectively equal . Let ABC be a spherical triangle ; produce the radii through its angles beyond the centre to meet the sphere in A'B'C ' ; then the sides and angles of ABC , A'B'C ' are respectively equal ...
Σελίδα 204
... symmetrical tri- angles ; but they cannot be applied to each other unless CB ' = CA = CB ; that is , unless they are isosceles . student may see this by constructing sym- metrical triangles on a spherical blackboard . Though equal ...
... symmetrical tri- angles ; but they cannot be applied to each other unless CB ' = CA = CB ; that is , unless they are isosceles . student may see this by constructing sym- metrical triangles on a spherical blackboard . Though equal ...
Σελίδα 205
... symmetrical triangle DFG ; then , as in ( I. 4 ) , it may be proved equal to DEF or DFG . But DEF is equal to DFG ( IX . 8 ) . Hence , ABC is equal in either case in all its parts to DEF . Proposition 10 . Theorem . If two triangles ...
... symmetrical triangle DFG ; then , as in ( I. 4 ) , it may be proved equal to DEF or DFG . But DEF is equal to DFG ( IX . 8 ) . Hence , ABC is equal in either case in all its parts to DEF . Proposition 10 . Theorem . If two triangles ...
Σελίδα 233
... symmetrical point in the other . The following propositions are easily deduced . The student should prove them : 0 A * B P 0 P 1. If one of two symmetrical lines intersect the axis of symmetry , the other intersects it in the same point ...
... symmetrical point in the other . The following propositions are easily deduced . The student should prove them : 0 A * B P 0 P 1. If one of two symmetrical lines intersect the axis of symmetry , the other intersects it in the same point ...
Άλλες εκδόσεις - Προβολή όλων
The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ... Isaac Sharpless Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ... Isaac Sharpless Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2017 |
Συχνά εμφανιζόμενοι όροι και φράσεις
A-BCD AB² ABCD AC² altitude angle ABC angle ACB angle BAC apothem bisect centre of similitude chord circle ABC circumference cone Corollary cylinder decagon describe diagonals diameter divided draw equal angles equiangular feet figure four right angles frustum given circle given straight line greater Hence inscribed interior angles intersect isosceles Let ABC line joining meet middle point multiplied number of sides opposite angles parallelogram parallelopiped pass perimeter perpendicular plane pole polyedron prism produced Prop proportional Proposition 12 Proposition 13 pyramid quadrilateral radical axis radii radius rectangle contained regular polygon right angles Scholium segment semicircle similar slant height solid solid angle sphere spherical angle spherical triangle square surface symmetrical tangent Theorem three angles three sides triangle ABC vertex
Δημοφιλή αποσπάσματα
Σελίδα 53 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Σελίδα 81 - On a given straight line to describe a segment of a circle, containing an angle equal to a given rectilineal angle. Let AB be the given straight line, and...
Σελίδα 31 - Any two angles of a triangle are together less than two right angles.
Σελίδα 128 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Σελίδα 15 - AXIOMS. 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals the wholes are equal. 3. If equals be taken from equals the remainders are equal.
Σελίδα 82 - To cut off a segment from a given circle which shall contain an angle equal to a given rectilineal angle. Let ABC be the given circle, and D the given rectilineal angle ; it is required to cut off a segment from the circle ABC that shall contain an angle equal to the given angle D.
Σελίδα 62 - If a straight line be divided into two equal, and also into two unequal parts ; the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section.
Σελίδα 166 - A be a solid angle contained by any number of plane angles BAC, CAD, DAE, EAF, FAB: these together are less than four right angles. Let the planes...
Σελίδα 15 - LET it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line.
Σελίδα 120 - Similar polygons may be divided into the same number of similar triangles, having the same ratio to one another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have.