Euclid's plane geometry, practically applied; book i, with explanatory notes, by H. Green1863 |
From inside the book
Results 1-5 of 30
Page 3
... line ; a wall , or a hedge , or a mound of earth , their boundary . The ... B.C. 323-283 . To him belongs the glory , for such it is , of having ... line ; the eleventh and twelfth , on the Elements of Solids ; and the thirteenth , on the ...
... line ; a wall , or a hedge , or a mound of earth , their boundary . The ... B.C. 323-283 . To him belongs the glory , for such it is , of having ... line ; the eleventh and twelfth , on the Elements of Solids ; and the thirteenth , on the ...
Page 8
... line BC , are each equal to the same line AB ; and 3rd , the inference , or thing proved , is , that the line AC equals the line BC , ie . , the two lines AC and BC are equal to each other . Here in the premisses two things are laid ...
... line BC , are each equal to the same line AB ; and 3rd , the inference , or thing proved , is , that the line AC equals the line BC , ie . , the two lines AC and BC are equal to each other . Here in the premisses two things are laid ...
Page 17
... line . The SOLUTION requires Pst . 3 , Pst . 1. - The DEMONSTRATION . - Def . 15 , Ax . 1 . E.1 , Dat . Given the st ... BC , each = AB ; BA ; BCD , .. AC = ACE , .. BC : AB , .. AC BC . = Thus AB , BC , and AC , sides of a △ , are ...
... line . The SOLUTION requires Pst . 3 , Pst . 1. - The DEMONSTRATION . - Def . 15 , Ax . 1 . E.1 , Dat . Given the st ... BC , each = AB ; BA ; BCD , .. AC = ACE , .. BC : AB , .. AC BC . = Thus AB , BC , and AC , sides of a △ , are ...
Page 18
... line AL = the given st . line BC . Q. E. F. SCHOLIUM . - When the given point is out of the given line , or its production , this problem admits of eight cases ; out if the given point is in the given line , or its production , of only ...
... line AL = the given st . line BC . Q. E. F. SCHOLIUM . - When the given point is out of the given line , or its production , this problem admits of eight cases ; out if the given point is in the given line , or its production , of only ...
Page 19
... line KL , and from K set off ten equal parts , as in KO ; then from O set ... lines may be readily measured . f 4. To use a Scale of Equal Parts intelligently ... BC = 45 $ 2 . EF ; and A ABC = A DEF ; 3. also ABC = / DEF , and ACB - ZDFE ...
... line KL , and from K set off ten equal parts , as in KO ; then from O set ... lines may be readily measured . f 4. To use a Scale of Equal Parts intelligently ... BC = 45 $ 2 . EF ; and A ABC = A DEF ; 3. also ABC = / DEF , and ACB - ZDFE ...
Common terms and phrases
AB² ABCD adjacent angles altitude angle equal angular point Axiom base BC bisected centre circle circumference coincide CON.-Pst Conc construct Deansgate diagonal diameter divided drawn equal bases equal sides equal triangles equil Euclid exterior angle four rt given line given point given st hypotenuse inference interior angles intersect JOHN HEYWOOD join 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 Scale of Equal side AC sides and angles square straight line surface Syene Theodolite theorem thing vertex Wherefore
Popular passages
Page 36 - 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.
Page 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...
Page 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.
Page 41 - We assume that but one straight line can be drawn through a given point parallel to a given straight line.
Page 13 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Page 16 - LET it be granted that a straight line may be drawn from any one point to any other point.
Page 54 - 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.
Page 21 - 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.
Page 22 - 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.
Page 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.