The Elements of Plane Geometry ...W.S. Sonnenschein and Company, 1884 |
Dentro del libro
Resultados 1-5 de 37
Página 30
... produced , the exterior angle is greater than either of the interior opposite angles . Let ABC be a triangle having the side BC produced to D : E 4 . B then shall the exterior angle ACD be greater than either of the interior opposite ...
... produced , the exterior angle is greater than either of the interior opposite angles . Let ABC be a triangle having the side BC produced to D : E 4 . B then shall the exterior angle ACD be greater than either of the interior opposite ...
Página 31
... produced . Again , produce AC to G , then , in like manner , the angle BCG is greater than the angle ABC which is opposite to AC , but the angle BCG is equal to the angle ACD , because they are vertically opposite ; therefore the angle ...
... produced . Again , produce AC to G , then , in like manner , the angle BCG is greater than the angle ABC which is opposite to AC , but the angle BCG is equal to the angle ACD , because they are vertically opposite ; therefore the angle ...
Página 32
... 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 angle ACB , then the angles ACD , ACB are together greater than the angles АВС ...
... 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 angle ACB , then the angles ACD , ACB are together greater than the angles АВС ...
Página 35
... Produce BA to D , make AD equal to AC , and join CD . Because AD is equal to AC , therefore the angle ACD is equal to the angle ADC ; but the angle BCD is greater than the angle ACD , I. 7 . Ax . a . therefore the angle BCD is also ...
... Produce BA to D , make AD equal to AC , and join CD . Because AD is equal to AC , therefore the angle ACD is equal to the angle ADC ; but the angle BCD is greater than the angle ACD , I. 7 . Ax . a . therefore the angle BCD is also ...
Página 36
... Produce BD to meet AC at E. Then BA and AE are together greater than BE , to each of these add EC , 1. 13 . then BA and AC are together greater than BE and EC ; Ax . f . again , DE and EC are together greater than DC 36 THE ELEMENTS OF ...
... Produce BD to meet AC at E. Then BA and AE are together greater than BE , to each of these add EC , 1. 13 . then BA and AC are together greater than BE and EC ; Ax . f . again , DE and EC are together greater than DC 36 THE ELEMENTS OF ...
Otras ediciones - Ver todas
Términos y frases comunes
AB is equal ABCD AC is equal adjacent angles adjoining sides alternate angle angle ABC angle ACB angle AFG angle BAC angle CAB angle DEF angle EDF angle FGD angles are equal angles equal BA and AC base BC bisectors bisects centre circle cutting Constr construct a triangle contrapositive diagonal equal angles equal to AC exterior angle find the locus Geometry given angle given point given straight line greater Hence hypotenuse identically equal interior opposite angle isosceles triangle less Let ABC meet middle point obtuse angle opposite sides parallel straight lines parallelogram perpendicular point equidistant Prob produced quadrilateral radius rectangle contained rectangle whose base right angles right-angled triangle shew side AB side AC side DF sides equal square on AC squares on AB straight angle straight line drawn Theorem trapezium triangle ABC triangle DEF triangles are identically twice the rectangle vertex
Pasajes populares
Página 27 - 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 70 - 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 56 - ... is equal to twice as many right angles as the polygon
Página 101 - Prove that parallelograms on the same base and between the same parallels are equal in area.
Página 35 - Any two sides of a triangle are together greater than the third side.
Página 26 - The lines drawn from the extremities of the base of an isosceles triangle to the middle points of the opposite sides are equal.
Página 70 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Página 85 - The locus of a point at a given distance from a given point is the circumference described from the point with the given distance as radius.
Página 42 - 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 110 - 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.