The elements of plane geometry, Τόμος 1 |
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Σελίδα 72
... Post . 3 . With centres D and E , and with any radius greater than half the straight line DE , draw circles , Post . 3 . let F be a point of intersection of these circles which lies within the angle BAC ; join AF : then shall AF bisect ...
... Post . 3 . With centres D and E , and with any radius greater than half the straight line DE , draw circles , Post . 3 . let F be a point of intersection of these circles which lies within the angle BAC ; join AF : then shall AF bisect ...
Σελίδα 73
... Post . 3 . With centres D and E , and with any radius greater than AD or AE , draw circles , Post . 3 . let F be a point of intersection of these circles ; Post . I. join AF : then shall AF be perpendicular to BAC . Join DF , EF . Then ...
... Post . 3 . With centres D and E , and with any radius greater than AD or AE , draw circles , Post . 3 . let F be a point of intersection of these circles ; Post . I. join AF : then shall AF be perpendicular to BAC . Join DF , EF . Then ...
Σελίδα 74
... Post . 3 . with centres E and F and the same radius as before draw circles cutting one another , on the side of AB remote from C , at G , Post . 3 . join CG cutting AB at H : then shall CH be perpendicular to AB . Join CE , CF , EG , FG ...
... Post . 3 . with centres E and F and the same radius as before draw circles cutting one another , on the side of AB remote from C , at G , Post . 3 . join CG cutting AB at H : then shall CH be perpendicular to AB . Join CE , CF , EG , FG ...
Σελίδα 75
... Post . 3 . join CD , cutting AB at E : Post . 1 . then shall AB be bisected at E. Join AC , AD , BC , BD . Then in the triangles ACD , BCD , Post . I. the side AC is equal to the side BC , the side AD is equal to the side BD , Constr ...
... Post . 3 . join CD , cutting AB at E : Post . 1 . then shall AB be bisected at E. Join AC , AD , BC , BD . Then in the triangles ACD , BCD , Post . I. the side AC is equal to the side BC , the side AD is equal to the side BD , Constr ...
Σελίδα 76
... Post . 3 . with centre A and the same radius draw a circle cutting BC at K , Post . 3 . with centre K and radius equal to GH draw a circle cutting the last circle at L , join AL : then shall AL make with BC an angle equal to DEF . Post ...
... Post . 3 . with centre A and the same radius draw a circle cutting BC at K , Post . 3 . with centre K and radius equal to GH draw a circle cutting the last circle at L , join AL : then shall AL make with BC an angle equal to DEF . Post ...
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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 bisector bisects centre circle cutting Constr construct a triangle contrapositive diagonal distance draw a circle equal angles equal to AC equal to CD 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 rectangle contained rectangle whose base right angles right-angled triangle shew side AB side AC sides equal square on AC squares on AB straight line drawn Theorem trapezium triangle ABC triangles are identically twice the rectangle vertex
Δημοφιλή αποσπάσματα
Σελίδα 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. either the sides adjacent to the equal...
Σελίδα 98 - 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.
Σελίδα 56 - ... is equal to twice as many right angles as the polygon
Σελίδα 35 - Any two sides of a triangle are together greater than the third side.
Σελίδα 26 - The straight lines drawn from the extremities of the base of an isosceles triangle to the middle points of the opposite sides are equal to one another.
Σελίδα 37 - 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.
Σελίδα 70 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Σελίδα 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.
Σελίδα 31 - Any two angles of a triangle are together less than two right angles.
Σελίδα 115 - In a right.angled triangle, the square on the hypotenuse is equal to the sum of the squares on the sides containing the right angle . . . . 130 Applications of Pythagoras' theorem . . . . 132 THEOREM 6.