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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Resultat 1-5 av 35
Side 277
... intersect at O , and the rectangle AO , OB be equal to the rectangle CO , OD , the circum- ference of a circle will pass through the four points A , B , C , D. For a circle may be described round the triangle ABC , by IV . 5 ; and then ...
... intersect at O , and the rectangle AO , OB be equal to the rectangle CO , OD , the circum- ference of a circle will pass through the four points A , B , C , D. For a circle may be described round the triangle ABC , by IV . 5 ; and then ...
Side 293
... , DB , and twice the square on DC , together with twice the rectangle AD , DE . But AD is equal to DB . Therefore the squares on AC , BC are equal to twice the squares on AD , DC . 2. If two chords intersect within a circle , the.
... , DB , and twice the square on DC , together with twice the rectangle AD , DE . But AD is equal to DB . Therefore the squares on AC , BC are equal to twice the squares on AD , DC . 2. If two chords intersect within a circle , the.
Side 294
... intersect within a circle , the angle which they include is measured by half the sum of the in- tercepted arcs . Let the chords AB and CD of a circle intersect at E ; join AD . The angle AEC is equal to the angles ADE , and DAE , by I ...
... intersect within a circle , the angle which they include is measured by half the sum of the in- tercepted arcs . Let the chords AB and CD of a circle intersect at E ; join AD . The angle AEC is equal to the angles ADE , and DAE , by I ...
Side 295
... intersect . When each of the given circles is without the other we can obtain two other solutions . For , describe a circle with A as a centre and radius equal to the sum of the radii of the given circles ; and continue as before ...
... intersect . When each of the given circles is without the other we can obtain two other solutions . For , describe a circle with A as a centre and radius equal to the sum of the radii of the given circles ; and continue as before ...
Side 305
... intersect the smaller circle again at K ; then AK is parallel_to_BH ( 14 ) ; therefore the angle AKT is equal to the angle BHG ; and the angle AKG is equal to the angle AGK , which is equal to the angle OGH , which is equal to the angle ...
... intersect the smaller circle again at K ; then AK is parallel_to_BH ( 14 ) ; therefore the angle AKT is equal to the angle BHG ; and the angle AKG is equal to the angle AGK , which is equal to the angle OGH , which is equal to the angle ...
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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 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 35 - 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.
Side 67 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle, is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle, Let ABC be an obtuse-angled triangle, having the obtuse angle...
Side 73 - 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 284 - 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 50 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Side 57 - 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 on the line between the points of section, is equal to the square on half the line.
Side 10 - 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 227 - If two straight lines be at right angles to the same plane, they shall be parallel to one another. Let the straight lines AB, CD be at right angles to the same plane : AB is parallel to CD.
Side 102 - 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 352 - 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.