The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Six Books and Portions of the Eleventh and Twelfth Books : with Notes, an Appendix, and ExercisesMacmillan, 1883 - 400 sider |
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Side 4
... triangle is that which has three unequal sides : 27. A right - angled triangle is that which has a right angle : [ The side opposite to the right angle in a right - angled triangle is fre- quently called the hypotenuse . ] 28. An obtuse ...
... triangle is that which has three unequal sides : 27. A right - angled triangle is that which has a right angle : [ The side opposite to the right angle in a right - angled triangle is fre- quently called the hypotenuse . ] 28. An obtuse ...
Side 16
... triangle DFE , and join CF. [ I. 1 . The straight line CF drawn from the given point C shall be at right angles to the given straight line AB . Because DC is equal to CE , [ Construction . and CF is common to the two triangles DCF , ECF ...
... triangle DFE , and join CF. [ I. 1 . The straight line CF drawn from the given point C shall be at right angles to the given straight line AB . Because DC is equal to CE , [ Construction . and CF is common to the two triangles DCF , ECF ...
Side 20
... right angles . A [ I. 13 . Again , because the straight line DE makes with ... triangle be produced , the exterior angle shall be greater than either of ... angle AEB is equal to the angle CEF 20 EUCLID'S ELEMENTS .
... right angles . A [ I. 13 . Again , because the straight line DE makes with ... triangle be produced , the exterior angle shall be greater than either of ... angle AEB is equal to the angle CEF 20 EUCLID'S ELEMENTS .
Side 21
... angle BCG , that is the angle ACD , is greater than the angle ABC . [ I. 15 . Wherefore , if one side & c . Q.E.D. PROPOSITION 17. THEOREM . Any two angles of a triangle are together less than two right angles . Let ABC be a triangle ...
... angle BCG , that is the angle ACD , is greater than the angle ABC . [ I. 15 . Wherefore , if one side & c . Q.E.D. PROPOSITION 17. THEOREM . Any two angles of a triangle are together less than two right angles . Let ABC be a triangle ...
Side 35
... triangle be produced , the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are toge- ther equal to two right angles . Let ABC be a triangle , and let one of its sides BC ...
... triangle be produced , the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are toge- ther equal to two right angles . Let ABC be a triangle , and let one of its sides BC ...
Andre utgaver - Vis alle
The Elements of Euclid for the Use of Schools and Colleges Isaac Todhunter Uten tilgangsbegrensning - 1872 |
The Elements of Euclid for the Use of Schools and Colleges: Comprising the ... Euclid,Isaac Todhunter Uten tilgangsbegrensning - 1884 |
The Elements of Euclid for the Use of Schools and Colleges: Comprising the ... Euclid,Isaac Todhunter Uten tilgangsbegrensning - 1867 |
Vanlige uttrykk og setninger
ABCD AC is equal angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC bisects the angle centre chord circle ABC circle described circumference Construction Corollary describe a circle diameter double draw a straight equal angles equal to F equiangular equilateral equimultiples Euclid Euclid's Elements exterior angle given circle given point given straight line gnomon Hypothesis inscribed intersect isosceles triangle less Let ABC magnitudes middle point multiple opposite angles opposite sides parallelogram perpendicular plane polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION quadrilateral radius rectangle contained rectilineal figure remaining angle rhombus right angles right-angled triangle segment shew shewn side BC square on AC straight line &c straight line drawn tangent THEOREM touches the circle triangle ABC triangle DEF twice the rectangle vertex Wherefore
Populære avsnitt
Side 262 - 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 71 - 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 262 - To draw a straight line at right angles to a given straight line, from a given point in the same. Let AB be...
Side 182 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 8 - 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 298 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Side 58 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Side 60 - 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 in the point C, and into two unequal parts in the point D ; The squares on AD and DB shall be together double of AD»+DB
Side 242 - Let AB and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken more than its half, and from the remainder more than its half, and so on ; there shall at length remain a magnitude less than C. For C may be multiplied, so at length to become greater than AB.
Side 4 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.