The Elements of Plane and Solid Geometry: With Chapters on Mensuration and Modern GeometryPorter & Coates, 1879 - 266 σελίδες |
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Αποτελέσματα 1 - 5 από τα 13.
Σελίδα 91
... quantities form a proportion ; thus , : A C B D or A B C D. Hence a proportion is an equation with both members fractional . 3. Ratio may be direct or inverse . If x and y be two variable quantities , such that , as x increases , y ...
... quantities form a proportion ; thus , : A C B D or A B C D. Hence a proportion is an equation with both members fractional . 3. Ratio may be direct or inverse . If x and y be two variable quantities , such that , as x increases , y ...
Σελίδα 92
... Quantities are in continued proportion when a conse- quent of one ratio is the same as the antecedent of the next ... Quantities are in proportion alternately , when antece- dent is compared with antecedent , and consequent with con ...
... Quantities are in continued proportion when a conse- quent of one ratio is the same as the antecedent of the next ... Quantities are in proportion alternately , when antece- dent is compared with antecedent , and consequent with con ...
Σελίδα 93
... quantities be in proportion , the product of the extremes is equal to the product of the means . A B C D , AxD - B × C. Let then A C For , because multiplying by B × D , we have B D AxD = Bx C. Corollary 1. — If three quantities be in ...
... quantities be in proportion , the product of the extremes is equal to the product of the means . A B C D , AxD - B × C. Let then A C For , because multiplying by B × D , we have B D AxD = Bx C. Corollary 1. — If three quantities be in ...
Σελίδα 94
... quantities may form a propor- tion , one set being taken for the extremes and the other for the means . If then For ... quantities are proportional to the quantities . Let A and B be two quantities , and mA and mB equimul- tiples of them ...
... quantities may form a propor- tion , one set being taken for the extremes and the other for the means . If then For ... quantities are proportional to the quantities . Let A and B be two quantities , and mA and mB equimul- tiples of them ...
Σελίδα 95
... quantities are propor- tional to the quantities . This may be proved as the above by supposing m to be fractional . Proposition 4 . Theorem . If equimultiples be taken of the first and second terms of a proportion , and also of the ...
... quantities are propor- tional to the quantities . This may be proved as the above by supposing m to be fractional . Proposition 4 . Theorem . If equimultiples be taken of the first and second terms of a proportion , and also of the ...
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 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 lune 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 similar triangles slant height solid solid angle sphere spherical triangle square surface symmetrical tangent Theorem Theorem.-If 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.