Euclid's plane geometry, practically applied; book i, with explanatory notes, by H. Green1863 |
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Σελίδα 8
... BC , are each equal to the same line AB ; and 3rd , the inference , or thing proved , is , that the line AC equals ... base are equal ; " the very words , though not in the exact form of an hypothesis , directly imply the ...
... BC , are each equal to the same line AB ; and 3rd , the inference , or thing proved , is , that the line AC equals ... base are equal ; " the very words , though not in the exact form of an hypothesis , directly imply the ...
Σελίδα 14
... base , and BC the perpendicular . C F I AAA B D E G H 28. An Obtuse - angled Triangle is that which has an obtuse angle ; as 29. An Acute - angled Triangle is that which has three acute angles ; as , GHI . 30 . The right and the obtuse ...
... base , and BC the perpendicular . C F I AAA B D E G H 28. An Obtuse - angled Triangle is that which has an obtuse angle ; as 29. An Acute - angled Triangle is that which has three acute angles ; as , GHI . 30 . The right and the obtuse ...
Σελίδα 19
... bases , or third sides , equal ; and the two triangles shall be equal , and their angles shall be equal , each ... BC = EF ; and △ ABC = A DEF ; 3. also ABC = / DEF , 4 " 2 . " " 435 BAC = the base A D and ACB = ZDFE . B CE D. 1 ...
... bases , or third sides , equal ; and the two triangles shall be equal , and their angles shall be equal , each ... BC = EF ; and △ ABC = A DEF ; 3. also ABC = / DEF , 4 " 2 . " " 435 BAC = the base A D and ACB = ZDFE . B CE D. 1 ...
Σελίδα 20
... base BC does coincide with and the base EF : 11 D.2 . 5 , 6 , 10 And A B falling on and being equal to D E ; A C to DF ; and BC to EF , 12 Ax . 8 . ..A ABC coincides with and - A DEF . DEF . 13 Hyp.1 , D.10 Also , since D E coincides ...
... base BC does coincide with and the base EF : 11 D.2 . 5 , 6 , 10 And A B falling on and being equal to D E ; A C to DF ; and BC to EF , 12 Ax . 8 . ..A ABC coincides with and - A DEF . DEF . 13 Hyp.1 , D.10 Also , since D E coincides ...
Σελίδα 22
... base . Wherefore , the angles at the base , & c . D. 1 by Def . 24 , P. 5 equilateral triangle is also equiangular . Let ABC be an equil . △ , AB = BC ... BC is common , and DBC = LACB ; = B D C .. DC = AB , and △ DBC = △ ABC . Thus ...
... base . Wherefore , the angles at the base , & c . D. 1 by Def . 24 , P. 5 equilateral triangle is also equiangular . Let ABC be an equil . △ , AB = BC ... BC is common , and DBC = LACB ; = B D C .. DC = AB , and △ DBC = △ ABC . Thus ...
Άλλες εκδόσεις - Προβολή όλων
Euclid's plane geometry, practically applied; book i, with explanatory notes ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 1897 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 43 - We assume that but one straight line can be drawn through a given point parallel to a given straight line.
Σελίδα 13 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Σελίδα 16 - LET it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.