The Elements of Plane GeometryS. Sonnenschein & Company, 1903 |
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Página 3
... meet a steadily continuing demand , a new edition has been published . It was felt , however , by many members of the Association that , in order to secure for the Syllabus more general consideration and acceptance , it was desirable ...
... meet a steadily continuing demand , a new edition has been published . It was felt , however , by many members of the Association that , in order to secure for the Syllabus more general consideration and acceptance , it was desirable ...
Página 14
... meet in one point cannot meet again unless they coincide . SECTION I ANGLES AT A POINT [ An angle is a simple concept incapable of definition , properly so - called , but the nature of the concept may be explained as follows , and for ...
... meet in one point cannot meet again unless they coincide . SECTION I ANGLES AT A POINT [ An angle is a simple concept incapable of definition , properly so - called , but the nature of the concept may be explained as follows , and for ...
Página 33
... BAC . Produce BD to meet AC at E. Then BA and AE are together greater than BE , to each of these add EC , then BA and AC are together greater than BE and EC I. 13 . Ax . f . again , DE and EC are together greater than DC TRIANGLES 33.
... BAC . Produce BD to meet AC at E. Then BA and AE are together greater than BE , to each of these add EC , then BA and AC are together greater than BE and EC I. 13 . Ax . f . again , DE and EC are together greater than DC TRIANGLES 33.
Página 37
... A let the line that bisects the angle FDC ' meet EF at G , join C'G . Then , in the triangles C'DG , FDG , the side C'D is equal to the side DF , the side DG is common to both , and the angle C'DG is equal to the angle FDG TRIANGLES 37.
... A let the line that bisects the angle FDC ' meet EF at G , join C'G . Then , in the triangles C'DG , FDG , the side C'D is equal to the side DF , the side DG is common to both , and the angle C'DG is equal to the angle FDG TRIANGLES 37.
Página 45
... meet in a point which is equidistant from the vertices of the triangle . * 33 . The bisectors of the angles of a triangle meet in a point which is equidistant from the sides of the triangle . * 34 . The bisectors of an angle of a ...
... meet in a point which is equidistant from the vertices of the triangle . * 33 . The bisectors of the angles of a triangle meet in a point which is equidistant from the sides of the triangle . * 34 . The bisectors of an angle of a ...
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Términos y frases comunes
ABCD AC is equal adjacent angles altitude angle ABC angle ACB angle BAC angle DAE angle DEF angle equal angle HBK base bisectors chord HK circle ABC circle whose centre circles DEF circles touch circumscribed circle coincide Constr diagonal diameter distance equal circles equal to AC equiangular exterior angle externally given angle given circle given point given ratio given straight line greater Hence hypotenuse identically equal inscribed circle isosceles triangle less Let ABC line joining magnitudes meet the circumference middle point minor arc multiple nine-points circle opposite angle opposite sides orthocentre parallelogram perpendicular point of contact polygon Prob produced proportional Prove Q.E.D. THEOR quadrilateral radii radius ratio compounded rectangle AC rectangle contained rectilineal figure rhombus right angles Shew side BC squares on BD straight line drawn tangent Theorem triangle ABC triangle DEF twice the rectangle vertical angle
Pasajes populares
Página 41 - 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 182 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle,. shall be equal to the square of the line which touches it.
Página 67 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Página 167 - 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 32 - Any two sides of a triangle are together greater than the third side.
Página 34 - Of all the straight lines that can be drawn to a given straight line from a given point outside it, the perpendicular is the shortest.
Página 23 - The lines drawn from the extremities of the base of an isosceles triangle to the middle points of the opposite sides are equal.
Página 63 - If there are three or more parallel straight lines, and the intercepts made by them on any straight line that cuts them are equal, then the corresponding intercepts on any other straight line that cuts them are also equal.
Página 39 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Página 106 - Iff 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.