A Text-book of Euclid's Elements for the Use of Schools. Books I.-VI. and XI, Libro 1Macmillan, 1900 - 456 páginas |
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Página 33
... middle point of the base is perpendicular to the base . 2. Shew that the straight lines which join the extremities of the base of an isosceles triangle to the middle points of the opposite sides , are equal to one another . 3. Two given ...
... middle point of the base is perpendicular to the base . 2. Shew that the straight lines which join the extremities of the base of an isosceles triangle to the middle points of the opposite sides , are equal to one another . 3. Two given ...
Página 50
... middle point of the base BC ; shew that the angle AXB is obtuse or acute , according as AB is greater or less than AČ . PROPOSITION 26. THEOREM . If two triangles have two angles 50 EUCLID'S ELEMENTS .
... middle point of the base BC ; shew that the angle AXB is obtuse or acute , according as AB is greater or less than AČ . PROPOSITION 26. THEOREM . If two triangles have two angles 50 EUCLID'S ELEMENTS .
Página 55
... point on the bisector of an angle is equidistant from the arms of the angle . 4. Through O , the middle point of a straight line AB , any straight line is drawn , and perpendiculars AX and BY are dropped upon it from A and B : shew that ...
... point on the bisector of an angle is equidistant from the arms of the angle . 4. Through O , the middle point of a straight line AB , any straight line is drawn , and perpendiculars AX and BY are dropped upon it from A and B : shew that ...
Página 65
... middle point of the hypotenuse . Hence the joining line is equal to half the hypotenuse . 5. Draw a straight line at right angles to a given finite straight line from one of its extremities , without producing the given straight line ...
... middle point of the hypotenuse . Hence the joining line is equal to half the hypotenuse . 5. Draw a straight line at right angles to a given finite straight line from one of its extremities , without producing the given straight line ...
Página 70
... point of a diagonal of a parallelogram and terminated by a pair of opposite sides , is bisected at that point . 11 ... middle points of the sides AD , BC ; shew that the figure AYCX is a parallelo- gram . MISCELLANEOUS EXERCISES ON ...
... point of a diagonal of a parallelogram and terminated by a pair of opposite sides , is bisected at that point . 11 ... middle points of the sides AD , BC ; shew that the figure AYCX is a parallelo- gram . MISCELLANEOUS EXERCISES ON ...
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Términos y frases comunes
ABCD AC is equal adjacent angles angle ABC angle ACB angle BAC angle equal base BC bisected bisectors centre chord circles intersect circumference circumscribed circle concyclic Constr Describe a circle diagonal diameter draw escribed circle Euclid's exterior angle find the locus given circle given point given straight line Given the base given triangle greater Hence hypotenuse inscribed isosceles triangle Let ABC line which joins meet middle point nine-points circle opposite angle opposite sides orthocentre par¹ parallelogram pedal triangle perp perpendiculars drawn point of contact polygon produced Proof PROPOSITION PROPOSITION 21 prove quadrilateral radical axis radius rectangle contained regular polygon rhombus right angles segment shew shewn side BC square straight line drawn subtended tangent THEOREM touch a given triangle ABC twice the rect vertex vertical angle
Pasajes populares
Página 42 - Any two sides of a triangle are together greater than the third side.
Página 162 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.
Página 162 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together •with the square...
Página 291 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Página 65 - 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 68 - And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB, therefore the whole angle ABD is equal to the whole angle ACD • (ax.
Página 143 - If 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.
Página 8 - Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same are equal to one another.
Página 79 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.
Página 242 - We may here notice that the perpendiculars from the vertices of a triangle to the opposite sides are concurrent; their meet is called the orthocentre, and the triangle obtained by joining the feet of the perpendiculars is called the pedal triangle.