Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids: to which are Added, Edlemnts of Plane and Spherical TrigonometryW.E. Dean, 1836 - 311 sider |
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Resultat 1-5 av 29
Side 36
... angles . Let ABC be a triangle , and let its side BC be pro- duced to D , the exterior angle ACD is greater than ei- ther of the interior oppo- site angles CBA , BAC . Bisecta AC in E , join BE and produce it to F , and make EF equal to ...
... angles . Let ABC be a triangle , and let its side BC be pro- duced to D , the exterior angle ACD is greater than ei- ther of the interior oppo- site angles CBA , BAC . Bisecta AC in E , join BE and produce it to F , and make EF equal to ...
Side 37
... angle ; any two of its angles together are less than two right angles . Produce BC to D ; and because ACD is the exterior angle of the tri- angle ABC , ACD is greater than the inte- a rior and opposite angle ABC ; to each of these B C a ...
... angle ; any two of its angles together are less than two right angles . Produce BC to D ; and because ACD is the exterior angle of the tri- angle ABC , ACD is greater than the inte- a rior and opposite angle ABC ; to each of these B C a ...
Side 39
... angle : therefore the side DB is greater than the Book 1 . side BC ; but DB is equal to BA and AC together ... exterior angle of a triangle is b 16.1 . greater than the interior and opposite angle , the exterior angle BDC of the triangle ...
... angle : therefore the side DB is greater than the Book 1 . side BC ; but DB is equal to BA and AC together ... exterior angle of a triangle is b 16.1 . greater than the interior and opposite angle , the exterior angle BDC of the triangle ...
Side 44
... angle GBC is equal to the angle DEF ; therefore the base GC is equal to the base DF , and the triangle GBC to the ... exterior angle BHA of the triangle AHC is equal to its inte- rior and opposite angle BCA : which is impossible b 44 ...
... angle GBC is equal to the angle DEF ; therefore the base GC is equal to the base DF , and the triangle GBC to the ... exterior angle BHA of the triangle AHC is equal to its inte- rior and opposite angle BCA : which is impossible b 44 ...
Side 45
... angle BCA : which is impossible b ; wherefore BC is not unequal to EF , that is , it is equal to it ; and AB is ... exterior angle AEF is greater than the interior and oppo- site angle EFG ; butA it is also equal to it , which is ...
... angle BCA : which is impossible b ; wherefore BC is not unequal to EF , that is , it is equal to it ; and AB is ... exterior angle AEF is greater than the interior and oppo- site angle EFG ; butA it is also equal to it , which is ...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ... Euclid,John Playfair Uten tilgangsbegrensning - 1853 |
Elements of Geometry: Containing the First Six Books of Euclid, with a ... Euclid,John Playfair Uten tilgangsbegrensning - 1851 |
Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1857 |
Vanlige uttrykk og setninger
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder definition demonstrated described diameter draw drawn equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism proportional proposition pyramid Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle spherical angle spherical triangle Spherical Trigonometry straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Populære avsnitt
Side 58 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Side 26 - If two triangles have two sides of the one equal to two sides of the...
Side 46 - Wherefore, if a straight line, &c. QED PROP. XXIX. THEOR. s«e N. Ij'a straight line fall upon two parallel straight lines, it makes the alternate angles equal...
Side 74 - THEOR. //' a straight line be divided into two equal, and also into two unequal parts, the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.
Side 84 - An angle in a segment is the angle contained by two straight lines drawn from any point in the circumference of the segment to the extremities of the straight . line which is the base of the segment.
Side 411 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Side 112 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Side 118 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Side 54 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Side 49 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are equal to two right angles.