The Elements of Plane Geometry ...W.S. Sonnenschein and Company, 1884 |
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Página 20
... AC be the arms of a straight angle , whose vertex is A , and DE , DF the arms of another straight angle , whose ... side of D as E , and C on the same side as F , or with C on the same side of D as E , and B on the same side as F , then ...
... AC be the arms of a straight angle , whose vertex is A , and DE , DF the arms of another straight angle , whose ... side of D as E , and C on the same side as F , or with C on the same side of D as E , and B on the same side as F , then ...
Página 25
... side the base . THEOR . 5. If two triangles have two sides of the one equal to two sides of the other , each to each ... AC to the side DF , and the angle BAC to the angle EDF : AAA B then shall the triangles be identically equal ...
... side the base . THEOR . 5. If two triangles have two sides of the one equal to two sides of the other , each to each ... AC to the side DF , and the angle BAC to the angle EDF : AAA B then shall the triangles be identically equal ...
Página 26
... AC falling along DF , C will fall on F , since AC is equal to DF . Hyp . Hence , B falling on E , and C on F , BC ... side BC equal to the side EF , the angle ACB to the angle DFF , and the angle ABC to the angle DEF . Q.E.D. Ex . 4. The ...
... AC falling along DF , C will fall on F , since AC is equal to DF . Hyp . Hence , B falling on E , and C on F , BC ... side BC equal to the side EF , the angle ACB to the angle DFF , and the angle ABC to the angle DEF . Q.E.D. Ex . 4. The ...
Página 27
... side EF : A E then shall the triangles be identically equal , having the angle BAC equal to the angle EDF , the side AC to the side DF , and the side AB to the side DE . Let the triangle ABC be applied to the triangle DEF , so that the ...
... side EF : A E then shall the triangles be identically equal , having the angle BAC equal to the angle EDF , the side AC to the side DF , and the side AB to the side DE . Let the triangle ABC be applied to the triangle DEF , so that the ...
Página 28
... side AC to the side DF , and the side AB to the side DE . Q.E.D. Ex . 10. If the bisector of an angle of a triangle is also perpendi- cular to the opposite side , the triangle is isosceles . THEOR . 7. If two sides of a triangle are ...
... side AC to the side DF , and the side AB to the side DE . Q.E.D. Ex . 10. If the bisector of an angle of a triangle is also perpendi- cular to the opposite side , the triangle is isosceles . THEOR . 7. If two sides of a triangle are ...
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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.