Euclid's plane geometry, practically applied; book i, with explanatory notes, by H. Green1863 |
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Página 7
... bisected by its diagonal , and subsidiary parallelograms are formed by two lines , one , parallel to one side , and the other , parallel to the other side , and both intersecting the diagonal , --the Complements of the Parallelogram are ...
... bisected by its diagonal , and subsidiary parallelograms are formed by two lines , one , parallel to one side , and the other , parallel to the other side , and both intersecting the diagonal , --the Complements of the Parallelogram are ...
Página 23
... . Again , * . * BC = BD , ../ BDC = BCD ; D CASE II . - Let the vertex D of △. 5 D. 3 . 6 D. 3 , 4 . but BDC is also > BCD ; ../ BDC is both and BCD , which is impossible Rec . Wherefore , the BAC is bisected by AF PROP . 7. - BOOK I. 23.
... . Again , * . * BC = BD , ../ BDC = BCD ; D CASE II . - Let the vertex D of △. 5 D. 3 . 6 D. 3 , 4 . but BDC is also > BCD ; ../ BDC is both and BCD , which is impossible Rec . Wherefore , the BAC is bisected by AF PROP . 7. - BOOK I. 23.
Página 25
... bisect a given. Rec . Wherefore , the BAC is bisected by AF . Q.E.F. SCH . - 1 . The bisection of the arc DGE , which measures an angle , is also effected by the bisection of the angle . 2. By successive bisections an angle may be ...
... bisect a given. Rec . Wherefore , the BAC is bisected by AF . Q.E.F. SCH . - 1 . The bisection of the arc DGE , which measures an angle , is also effected by the bisection of the angle . 2. By successive bisections an angle may be ...
Página 26
... bisect it . | On AB make an equil . △ ABC ; let CD make ACD = △ BCD , and meet AB ; then AD = BD , i.e , AB is ... bisected in D. Q.E.F. SCH . - Вy successive bisections a st . line may thus be divided into any number of equal ...
... bisect it . | On AB make an equil . △ ABC ; let CD make ACD = △ BCD , and meet AB ; then AD = BD , i.e , AB is ... bisected in D. Q.E.F. SCH . - Вy successive bisections a st . line may thus be divided into any number of equal ...
Página 51
... bisected by its diameter , 2 P. 35 . 3 P. 34 . .. the EBCA = the But a .. A ABC = half the and A DBC : = half the 4 Ax . 7 . also A ABC = △ DBC . 5 Rec . WEBCA , DBCF ; Wherefore , triangles upon the same base , & c . Q E.D. SCH . - On ...
... bisected by its diameter , 2 P. 35 . 3 P. 34 . .. the EBCA = the But a .. A ABC = half the and A DBC : = half the 4 Ax . 7 . also A ABC = △ DBC . 5 Rec . WEBCA , DBCF ; Wherefore , triangles upon the same base , & c . Q E.D. SCH . - On ...
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Términos y frases comunes
AB² ABCD adjacent angles altitude angle equal angular point base BC bisected centre circle circumference coincide CON.-Pst Conc construct Deansgate demonstration diagonal diameter distance divided draw drawn earth's equal bases equal sides equil Euclid exterior angle feet four rt given line given point given st hypotenuse inches inference intersect JOHN HEYWOOD join less let BC Let the st line BC line CD measure meet miles opposite angles parallel parallelogram perpendicular Plane Geometry produced PROP proposition proved Quæs rectangle rectil rectilineal angle rectilineal figure right angles sides and angles square straight line surface Syene Theodolite theorem thing vertex Wherefore
Pasajes populares
Página 38 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Página 17 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Página 17 - 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 43 - We assume that but one straight line can be drawn through a given point parallel to a given straight line.
Página 13 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Página 16 - LET it be granted that a straight line may be drawn from any one point to any other point.
Página 56 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Página 23 - If two angles of a triangle be equal to one another, the sides also which subtend, or are opposite to, the equal angles, shall be equal to one another.
Página 24 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base, equal to one another, and likewise those which are terminated in the other extremity.
Página 12 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.