A Text-book of Euclid's Elements for the Use of Schools. Books I.-VI. and XI, Bok 1Macmillan, 1900 - 456 sider |
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Side 13
... things which are equal to the same thing are equal to one another . Therefore AF is equal to BC ; and it has been drawn from the given point A. Ax . 1 . Q.E.F. PROPOSITION 3. PROBLEM . From the greater of two given BOOK I. 13 PROP . 2 .
... things which are equal to the same thing are equal to one another . Therefore AF is equal to BC ; and it has been drawn from the given point A. Ax . 1 . Q.E.F. PROPOSITION 3. PROBLEM . From the greater of two given BOOK I. 13 PROP . 2 .
Side 15
... Prop . 2 the point A may be joined to either extremity of the line BC ; the equilateral triangle may be described on ... PROPS . 1-3 . 15.
... Prop . 2 the point A may be joined to either extremity of the line BC ; the equilateral triangle may be described on ... PROPS . 1-3 . 15.
Side 17
... is a quadrilateral having the opposite sides BC , AD equal , and also the angle BCD equal to the angle ADC : prove that BD is equal to AC . H.S.E. B PROPOSITION 5. THEOREM . The angles at the base of BOOK I. PROP . 4 . 17.
... is a quadrilateral having the opposite sides BC , AD equal , and also the angle BCD equal to the angle ADC : prove that BD is equal to AC . H.S.E. B PROPOSITION 5. THEOREM . The angles at the base of BOOK I. PROP . 4 . 17.
Side 19
... the diagram . This difficulty may be diminished by detaching each pair of triangles from the rest of the figure , as shewn in the margin . F C B B F PROPOSITION 6. THEOREM . If two angles of a triangle BOOK I. PROP . 5 . 19.
... the diagram . This difficulty may be diminished by detaching each pair of triangles from the rest of the figure , as shewn in the margin . F C B B F PROPOSITION 6. THEOREM . If two angles of a triangle BOOK I. PROP . 5 . 19.
Side 21
... Prop . 5 it is assumed that AB = AC ; it is required to prove that the angle ABC = the angle ACB . Now in Prop . 6 it is assumed that the angle ABC = the angle ACB it is required to prove that AB = AC . } Thus we see that Prop . 6 is ...
... Prop . 5 it is assumed that AB = AC ; it is required to prove that the angle ABC = the angle ACB . Now in Prop . 6 it is assumed that the angle ABC = the angle ACB it is required to prove that AB = AC . } Thus we see that Prop . 6 is ...
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A Text-book of Euclid's Elements: For the Use of Schools : Parts ..., Bøker 1-6 Euclid,Henry Sinclair Hall,Frederick Haller Stevens Uten tilgangsbegrensning - 1889 |
A Text-book of Euclid's Elements for the Use of Schools. Books I ..., Bøker 1-6 Euclid,Henry Sinclair Hall,Frederick Haller Stevens Uten tilgangsbegrensning - 1898 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 42 - Any two sides of a triangle are together greater than the third side.
Side 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.
Side 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...
Side 291 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.