The Elements of Plane GeometryS. Sonnenschein & Company, 1903 |
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Page 12
... less than B , C is less than D. Three such Theorems having been demonstrated the converse of each is necessarily true . 10. Rule of Identity . If there is but one A , and but one B ; then from the fact that A is B it necessarily follows ...
... less than B , C is less than D. Three such Theorems having been demonstrated the converse of each is necessarily true . 10. Rule of Identity . If there is but one A , and but one B ; then from the fact that A is B it necessarily follows ...
Page 16
... less than a righ DEF . 13. An obtuse angle is that which is greater thar angle , but less than two right angles . DEF . 14. A reflex angle is a term sometimes used for a jugate angle . DEF . 15. When the sum of two angles is a right ang ...
... less than a righ DEF . 13. An obtuse angle is that which is greater thar angle , but less than two right angles . DEF . 14. A reflex angle is a term sometimes used for a jugate angle . DEF . 15. When the sum of two angles is a right ang ...
Page 29
... less then shall any two of its angles be together less than two right angles . Produce BC to D. Because ACD is an exterior angle of the triangle ABC , therefore it is greater than the interior opposite angle ABC , I. 9 . to each add the ...
... less then shall any two of its angles be together less than two right angles . Produce BC to D. Because ACD is an exterior angle of the triangle ABC , therefore it is greater than the interior opposite angle ABC , I. 9 . to each add the ...
Page 31
... less than AB , for then the angle ABC would be less than the angle ACB ; I. 11 . therefore AC is greater than AB . Q.E.D. NOTE . As to this proof and that of Ex . 15 of . Introduction , § 9 . Ex . 16. The hypotenuse of a right ...
... less than AB , for then the angle ABC would be less than the angle ACB ; I. 11 . therefore AC is greater than AB . Q.E.D. NOTE . As to this proof and that of Ex . 15 of . Introduction , § 9 . Ex . 16. The hypotenuse of a right ...
Page 33
... less than twice the sum of the diagonals . THEOR . 14. If from the ends of a side of a triangle two straight lines are drawn to a point within the triangle , these are together less than the two other sides of the triangle , but con ...
... less than twice the sum of the diagonals . THEOR . 14. If from the ends of a side of a triangle two straight lines are drawn to a point within the triangle , these are together less than the two other sides of the triangle , but con ...
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Common terms and phrases
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 touch circumscribed circle coincide Constr diagonal diameter distance divided duplicate ratio equal angles equal to AC equiangular exterior angle given angle given circle given point given straight line greater half the angle Hence hypotenuse identically equal inscribed circle isosceles triangle less Let ABC line joining magnitudes meet the circumference middle point minor arc opposite angles opposite sides parallelogram perpendicular point equidistant polygon Prob produced Prove quadrilateral radii radius ratio compounded rectangle contained rectilineal figure rhombus right angles segment BAC Shew side BC square on AC straight line drawn tangent THEOR Theorem triangle ABC triangle DEF twice the rectangle vertical angle Нур
Popular passages
Page 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.
Page 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.
Page 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.
Page 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.
Page 32 - Any two sides of a triangle are together greater than the third side.
Page 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.
Page 23 - The lines drawn from the extremities of the base of an isosceles triangle to the middle points of the opposite sides are equal.
Page 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.
Page 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.
Page 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.