Euclid's plane geometry, practically applied; book i, with explanatory notes, by H. Green1863 |
Dentro del libro
Resultados 1-5 de 23
Página 18
... Wherefore from the given . A there has been drawn a st . 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 ...
... Wherefore from the given . A there has been drawn a st . 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 ...
Página 20
... Wherefore , if two triangles have two sides , & c . Q.E.D. SCH . - 1 , This being the first Theorem , it is exclusively proved by means of the Axioms . The converse of the 8th Axiom is assumed ; namely , that if the magnitudes are equal ...
... Wherefore , if two triangles have two sides , & c . Q.E.D. SCH . - 1 , This being the first Theorem , it is exclusively proved by means of the Axioms . The converse of the 8th Axiom is assumed ; namely , that if the magnitudes are equal ...
Página 22
... 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 = AC ; then shall its angles be equal , LA to B to / C . Since A B = A C , Q.E.D. .. < B ...
... 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 = AC ; then shall its angles be equal , LA to B to / C . Since A B = A C , Q.E.D. .. < B ...
Página 23
... Wherefore , every equiangular triangle , & c . Q.E.D. SCH . 1. Converse theorems are not universally true ; for instance , the direct proposition is universally true , - " If two triangles have their three sides respectively equal , the ...
... Wherefore , every equiangular triangle , & c . Q.E.D. SCH . 1. Converse theorems are not universally true ; for instance , the direct proposition is universally true , - " If two triangles have their three sides respectively equal , the ...
Página 24
... Wherefore ,. BC coincides with EF , BA and CA shall coincide with ED , FD . For , suppose that BC coincides with EF , but not BA and CA with ED , FD , but with other lines , as EG , FG , D. 5 by Conc . 6 7 P. 7 . 24 EUCLID'S ELEMENTS .
... Wherefore ,. BC coincides with EF , BA and CA shall coincide with ED , FD . For , suppose that BC coincides with EF , but not BA and CA with ED , FD , but with other lines , as EG , FG , D. 5 by Conc . 6 7 P. 7 . 24 EUCLID'S ELEMENTS .
Otras ediciones - Ver todas
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.