The Elements of Euclid for the Use of Schools and Colleges: With Notes, an Appendix, and Exercises. comprising the first six books and portions of the eleventh and twelfth booksMacmillan and Company, 1880 - 400 páginas |
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Página 254
... respectively required for the first time . The first book is chiefly devoted to the properties of triangles and parallelograms . We may observe that Euclid himself does not distinguish between problems and theorems except by using at ...
... respectively required for the first time . The first book is chiefly devoted to the properties of triangles and parallelograms . We may observe that Euclid himself does not distinguish between problems and theorems except by using at ...
Página 260
... respectively equal to all the angles of the other , each to each , and have also a side of the one , opposite to any angle , equal to the side opposite to the equal angle in the other , the triangles shall be equal in all respects . The ...
... respectively equal to all the angles of the other , each to each , and have also a side of the one , opposite to any angle , equal to the side opposite to the equal angle in the other , the triangles shall be equal in all respects . The ...
Página 330
... respective circles . Hence the square on PA exceeds the square on PB , by a known square , namely a square equal to the excess of the square on the radius of the circle of which A is the centre over the square on the radius of the ...
... respective circles . Hence the square on PA exceeds the square on PB , by a known square , namely a square equal to the excess of the square on the radius of the circle of which A is the centre over the square on the radius of the ...
Página 342
... respectively parallel to two others C and D , shew that the inclination of A to B is equal to that of C to D. 36. A straight line is drawn terminated by two parallel straight lines ; through its middle point any straight line is drawn ...
... respectively parallel to two others C and D , shew that the inclination of A to B is equal to that of C to D. 36. A straight line is drawn terminated by two parallel straight lines ; through its middle point any straight line is drawn ...
Página 346
... respectively equal to two given straight lines . How many such points are there ? 86. It is required to draw a straight line which shall be equal to one straight line and parallel to another , and be terminated by two given straight ...
... respectively equal to two given straight lines . How many such points are there ? 86. It is required to draw a straight line which shall be equal to one straight line and parallel to another , and be terminated by two given straight ...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ... Issac Todhunter Sin vista previa disponible - 2014 |
Términos y frases comunes
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
Pasajes populares
Página 225 - 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.
Página 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.
Página 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.
Página 39 - Triangles upon the same base, and between the same parallels, are equal to one another.
Página 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.
Página 353 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.
Página 67 - ... 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 ACB; and from the point A, let AD be drawn perpendicular to BC produced.
Página 300 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Página xv - PROPOSITION I. PROBLEM. To describe an equilateral triangle upon a given Jinite straight line. Let AB be the given straight line. It is required to describe an equilateral triangle upon AB, From the centre A, at the distance AB, describe the circle BCD ; (post.
Página 36 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.