Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with Explanatory Notes; a Series of Questions on Each Book; and a Selection of Geometrical Exercises from the Senate-house and College Examination Papers, with Hints, &c. Designed for the Use of the Junior Classes in Public and Private Schools. the first six books, and the portions of the eleventh and twelfth books read at CambridgeLongman, Green, Longman, Roberts, and Green, 1868 - 410 sider |
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Resultat 1-5 av 100
Side 11
... greater than the other . If possible , let AB be greater than AC ; and from BA cut off BD equal to CA the less , ( 1. 3. ) and join DC . Then , in the triangles DBC , ABC , because DB is equal to AC , and BC is common to both triangles ...
... greater than the other . If possible , let AB be greater than AC ; and from BA cut off BD equal to CA the less , ( 1. 3. ) and join DC . Then , in the triangles DBC , ABC , because DB is equal to AC , and BC is common to both triangles ...
Side 12
... greater than the angle BCD ; ( ax . 9. ) therefore also the angle FDC is greater than the angle BCD ; much more then is the angle BDC greater than the angle BCD . Again , because BC is equal to BD in the triangle BCD , therefore the ...
... greater than the angle BCD ; ( ax . 9. ) therefore also the angle FDC is greater than the angle BCD ; much more then is the angle BDC greater than the angle BCD . Again , because BC is equal to BD in the triangle BCD , therefore the ...
Side 17
... greater than either of the interior opposite angles . Let ABC be a triangle , and let the side BC be produced to D. Then the exterior angle ACD shall be greater than either of the interior opposite angles ČBA or BAC . Α F A. B G Bisect ...
... greater than either of the interior opposite angles . Let ABC be a triangle , and let the side BC be produced to D. Then the exterior angle ACD shall be greater than either of the interior opposite angles ČBA or BAC . Α F A. B G Bisect ...
Side 18
... greater than the angle ECF ; therefore the angle ACD is greater than the angle BAE or BAC . In the same manner , if the side BC be bisected , and AC be pro- duced to G ; it may be demonstrated that the angle BCG , that is , the angle ...
... greater than the angle ECF ; therefore the angle ACD is greater than the angle BAE or BAC . In the same manner , if the side BC be bisected , and AC be pro- duced to G ; it may be demonstrated that the angle BCG , that is , the angle ...
Side 19
... greater than the interior and opposite angle DCB ; ( 1. 16. ) but the angle ADB has been proved equal to the angle ABD , therefore the angle ABD is greater than the angle DCB ; wherefore much more is the angle ABC greater than the angle ...
... greater than the interior and opposite angle DCB ; ( 1. 16. ) but the angle ADB has been proved equal to the angle ABD , therefore the angle ABD is greater than the angle DCB ; wherefore much more is the angle ABC greater than the angle ...
Vanlige uttrykk og setninger
A₁ ABCD AC is equal Algebraically angle ABC angle ACB angle BAC Apply Euc base BC chord circle ABC constr demonstrated describe a circle diagonals diameter divided double draw equal angles equiangular equilateral triangle equimultiples Euclid exterior angle Geometrical given circle given line given point given straight line gnomon greater hypotenuse inscribed intersection isosceles triangle less Let ABC line BC lines be drawn multiple opposite angles parallelogram parallelopiped pentagon perpendicular plane polygon problem produced Prop proportionals proved Q.E.D. PROPOSITION quadrilateral figure radius ratio rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn similar similar triangles solid angle square on AC tangent THEOREM touch the circle trapezium triangle ABC twice the rectangle vertex vertical angle wherefore
Populære avsnitt
Side 6 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Side 118 - Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.
Side 2 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Side 317 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Side 90 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.
Side 88 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Side 30 - ... twice as many right angles as the figure has sides ; therefore all the angles of the figure together with four right angles, are equal to twice as many right angles as the figure has sides.
Side 9 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Side 22 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other...
Side 92 - 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. Let the straight line AB be divided into two equal parts...