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, 1867 - 400 sider |
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Side 19
... manner it may be shewn that no other can be in the same straight line with it but BD ; therefore BD is in the same straight line with CB . Wherefore , if at a point & c . Q.E.D. PROPOSITION 15. THEOREM . If two straight lines cut one ...
... manner it may be shewn that no other can be in the same straight line with it but BD ; therefore BD is in the same straight line with CB . Wherefore , if at a point & c . Q.E.D. PROPOSITION 15. THEOREM . If two straight lines cut one ...
Side 20
... manner it may be shewn that the angle CEB is equal to the angle AED . Wherefore , if two straight lines & c . Q.E.D. Corollary 1. From this it is manifest that , if two straight lines cut one another , the angles which they make at the ...
... manner it may be shewn that the angle CEB is equal to the angle AED . Wherefore , if two straight lines & c . Q.E.D. Corollary 1. From this it is manifest that , if two straight lines cut one another , the angles which they make at the ...
Side 21
... manner if BC be bisected , and the side AC be produced to G , it may be shewn that the 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 ...
... manner if BC be bisected , and the side AC be produced to G , it may be shewn that the 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 ...
Side 23
... manner it may be shewn that AB , BC are greater than AC , and BC , CĂ greater than AB . Wherefore , any two sides & c . Q.E.D. PROPOSITION 21 . THEOREM . If from the ends of the side of a triangle there be drawn two straight lines to a ...
... manner it may be shewn that AB , BC are greater than AC , and BC , CĂ greater than AB . Wherefore , any two sides & c . Q.E.D. PROPOSITION 21 . THEOREM . If from the ends of the side of a triangle there be drawn two straight lines to a ...
Side 31
... manner , it may be shewn that they do not meet towards A , C. But those straight lines which being produced ever so far both ways do not meet , are parallel . Therefore AB is parallel to CD . Wherefore , if a straight line & c . Q.E.D. ...
... manner , it may be shewn that they do not meet towards A , C. But those straight lines which being produced ever so far both ways do not meet , are parallel . Therefore AB is parallel to CD . Wherefore , if a straight line & c . Q.E.D. ...
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 - 1883 |
Vanlige uttrykk og setninger
ABCD angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC BC is equal 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 286 - 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 30 - 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. either the sides adjacent to the equal...
Side 34 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles...
Side 37 - 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 together equal to two right angles.
Side 12 - 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 302 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Side 220 - 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 354 - Prove that the square on any straight line drawn from the vertex of an isosceles triangle to the base, is less than the square on a side of the triangle by the rectangle contained by the segments of the base : and conversely.
Side 104 - 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 96 - The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles.