The Elements of Plane and Solid Geometry: With Chapters on Mensuration and Modern GeometryPorter & Coates, 1879 - 266 sider |
Inni boken
Resultat 1-5 av 34
Side 27
... A B C D ANALYSIS . ( By Hyp . ) , AB AC = ( By constr . ) , BAD CAD ( I. 7 ) , ABC = ACB . AD common . Corollary . — Every equilateral triangle is also equiangular . Proposition 14 . Theorem . — If two angles of a triangle be equal to ...
... A B C D ANALYSIS . ( By Hyp . ) , AB AC = ( By constr . ) , BAD CAD ( I. 7 ) , ABC = ACB . AD common . Corollary . — Every equilateral triangle is also equiangular . Proposition 14 . Theorem . — If two angles of a triangle be equal to ...
Side 44
... ABCD be a parallelogram , and EH , GF parallelo- grams about the diagonal ; then the complements BK , KD , which make up the whole figure , are equal to each other . Because AC is a diagonal , the triangles ABC , ADC are equal to each ...
... ABCD be a parallelogram , and EH , GF parallelo- grams about the diagonal ; then the complements BK , KD , which make up the whole figure , are equal to each other . Because AC is a diagonal , the triangles ABC , ADC are equal to each ...
Side 59
... ABCD be a parallelogram , and AC , BD its diagonals ; then AC2 + BD2 = AB2 + BC2 + CD2 + DA2 . Let AC and BD intersect each other in E ; and because the vertical angles AED , CEB are equal ( I. 17 ) , and also the alternate angles EAD ...
... ABCD be a parallelogram , and AC , BD its diagonals ; then AC2 + BD2 = AB2 + BC2 + CD2 + DA2 . Let AC and BD intersect each other in E ; and because the vertical angles AED , CEB are equal ( I. 17 ) , and also the alternate angles EAD ...
Side 61
... , and CE be cut off its diagonal equal to AB , and EF be drawn at right angles to CB , then BE- EF = FD . 5. The squares of the diagonals of a tra- A B C D pezium are together less than the squares of the four GEOMETRY . - BOOK II . 61.
... , and CE be cut off its diagonal equal to AB , and EF be drawn at right angles to CB , then BE- EF = FD . 5. The squares of the diagonals of a tra- A B C D pezium are together less than the squares of the four GEOMETRY . - BOOK II . 61.
Side 67
... ABCD be a circle , and AC , BD two straight lines in it which do not pass through the centre ; they will not bisect each other . For , if possible , let AE = EC and BE = ED . Take ( III . 1 ) F , the centre of the circle , and join EF ...
... ABCD be a circle , and AC , BD two straight lines in it which do not pass through the centre ; they will not bisect each other . For , if possible , let AE = EC and BE = ED . Take ( III . 1 ) F , the centre of the circle , and join EF ...
Andre utgaver - Vis alle
The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ... Isaac Sharpless Uten tilgangsbegrensning - 1882 |
The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ... Isaac Sharpless Ingen forhåndsvisning tilgjengelig - 2016 |
The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ... Isaac Sharpless Ingen forhåndsvisning tilgjengelig - 2017 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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...
Side 31 - Any two angles of a triangle are together less than two right angles.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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...
Side 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.
Side 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.