A Text-book of Euclid's Elements for the Use of Schools. Books I.-VI. and XI, Bücher 1Macmillan, 1900 - 456 Seiten |
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Seite 10
... divided into a number of separate discussions , called propositions . Propositions are of two kinds , Problems and Theorems . A Problem proposes to perform some geometrical construction , such as to draw some particular line , or to ...
... divided into a number of separate discussions , called propositions . Propositions are of two kinds , Problems and Theorems . A Problem proposes to perform some geometrical construction , such as to draw some particular line , or to ...
Seite 25
... BAC , BDC will be divided into two equal parts . 5. If in the figure of Ex . 4 the line AD meets BC in E , prove that BE EC . B PROPOSITION 8. ALTERNATIVE PROOF . Let ABC and DEF NOTE AND EXERCISES ON BOOK I. PROP S. 25.
... BAC , BDC will be divided into two equal parts . 5. If in the figure of Ex . 4 the line AD meets BC in E , prove that BE EC . B PROPOSITION 8. ALTERNATIVE PROOF . Let ABC and DEF NOTE AND EXERCISES ON BOOK I. PROP S. 25.
Seite 65
... divided into two isosceles triangles by a straight line drawn from the right angle to the 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 ...
... divided into two isosceles triangles by a straight line drawn from the right angle to the 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 ...
Seite 66
... divided into as many triangles as it has sides . And the three angles of each triangle are together equal to two right angles . I. 32 . Hence all the angles of all the triangles are together equal to twice as many right angles as the ...
... divided into as many triangles as it has sides . And the three angles of each triangle are together equal to two right angles . I. 32 . Hence all the angles of all the triangles are together equal to twice as many right angles as the ...
Seite 79
... divided by each of its medians into two parts of equal area . 6. A parallelogram is divided by its diagonals into four triangles of equal area . 7. ABC is a triangle , and its base BC is bisected at X ; if Y be any point in the median ...
... divided by each of its medians into two parts of equal area . 6. A parallelogram is divided by its diagonals into four triangles of equal area . 7. ABC is a triangle , and its base BC is bisected at X ; if Y be any point in the median ...
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 42 - Any two sides of a triangle are together greater than the third side.
Seite 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.
Seite 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...
Seite 291 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.