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 xii
... CONTACT OF CIRCLES . The Common Tangent to Two Circles , Problems on Tangency , Orthogonal Circles 233 235 III . ON ... Points Circle 297 303 II . MISCELLANEOUS EXAMPLES I. ON POLE AND POLAR APPENDIX . II . ON THE RADICAL AXIS . i V EUCLID'S ...
... CONTACT OF CIRCLES . The Common Tangent to Two Circles , Problems on Tangency , Orthogonal Circles 233 235 III . ON ... Points Circle 297 303 II . MISCELLANEOUS EXAMPLES I. ON POLE AND POLAR APPENDIX . II . ON THE RADICAL AXIS . i V EUCLID'S ...
Página 164
... points . 5. A tangent to a circle is a straight line which meets the circumference , but being produced , does not cut it . Such a line is said to touch the circle at a point ; and the point is called the point of contact . оо NOTE . If ...
... points . 5. A tangent to a circle is a straight line which meets the circumference , but being produced , does not cut it . Such a line is said to touch the circle at a point ; and the point is called the point of contact . оо NOTE . If ...
Página 165
... point will ultimately approach the fixed point P , until at length these points may be made to coincide . When the ... contact : when one of the circles is within the other , the first is said to touch the other internally , or to have ...
... point will ultimately approach the fixed point P , until at length these points may be made to coincide . When the ... contact : when one of the circles is within the other , the first is said to touch the other internally , or to have ...
Página 182
... point of contact . V B D Let ABC and ADE be two circles which touch one another internally at A ; let F be the ... point , but in no other ; that is , they must touch one another . 2. If two circles whose centres are A and B touch one ...
... point of contact . V B D Let ABC and ADE be two circles which touch one another internally at A ; let F be the ... point , but in no other ; that is , they must touch one another . 2. If two circles whose centres are A and B touch one ...
Página 183
... point of contact . B HAK E Let ABC and ADE be two circles which touch one another externally at A ; let F be the centre of the and G the centre of the O ADE . Then shall FG pass through A. ABC , Construction . For if not , suppose , if ...
... point of contact . B HAK E Let ABC and ADE be two circles which touch one another externally at A ; let F be the centre of the and G the centre of the O ADE . Then shall FG pass through A. ABC , Construction . For if not , suppose , if ...
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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.