An introduction to geometry, consisting of Euclid's Elements, book i, accompanied by numerous explanations, questions, and exercises, by J. Walmsley. [With] Answers, Volumen11884 |
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Página 3
... suppose that , in walking the whole distance , you never change your direction , what sort of line will you consider it to be ? 5. Suppose , on the other hand , while always looking along the line just in front of you , you find ...
... suppose that , in walking the whole distance , you never change your direction , what sort of line will you consider it to be ? 5. Suppose , on the other hand , while always looking along the line just in front of you , you find ...
Página 15
... Suppose OEU to be a right angle , then name the triangles EOU , EOT according to the nature of their angles . 10. Which side of the triangle EOU is the hypotenuse ? 11. If , also , each of the angles EFO , FOE is acute , say why FOE ...
... Suppose OEU to be a right angle , then name the triangles EOU , EOT according to the nature of their angles . 10. Which side of the triangle EOU is the hypotenuse ? 11. If , also , each of the angles EFO , FOE is acute , say why FOE ...
Página 30
... suppose we have AB upon DE , and we know that angle A is equal to angle D , where must AC fall if the triangle ABC be pressed down ? 11. Suppose the boundaries of one figure fit upon the boundaries of another , what is the inference ...
... suppose we have AB upon DE , and we know that angle A is equal to angle D , where must AC fall if the triangle ABC be pressed down ? 11. Suppose the boundaries of one figure fit upon the boundaries of another , what is the inference ...
Página 33
... Suppose in the triangles ABC , DEF the sides AB , DF are equal , also AC , DE , and angles BAC , EDF ; state the conclusion so far as regards the other angles ; that is , the third and fourth conclusions . 3. In the annexed figure ...
... Suppose in the triangles ABC , DEF the sides AB , DF are equal , also AC , DE , and angles BAC , EDF ; state the conclusion so far as regards the other angles ; that is , the third and fourth conclusions . 3. In the annexed figure ...
Página 36
... sides of the one triangle equal to two of the other . 8. Will this be sufficient to draw any conclusion from by the aid of Prop . IV . ? If not , say what more will be required . 9. Suppose now it is asserted that DB , BC 36 EUCLID BOOK I.
... sides of the one triangle equal to two of the other . 8. Will this be sufficient to draw any conclusion from by the aid of Prop . IV . ? If not , say what more will be required . 9. Suppose now it is asserted that DB , BC 36 EUCLID BOOK I.
Otras ediciones - Ver todas
An Introduction to Geometry, Consisting of Euclid's Elements, Book I ... Euclides Sin vista previa disponible - 2013 |
An Introduction to Geometry, Consisting of Euclid's Elements, Book I ... Euclides Sin vista previa disponible - 2023 |
An Introduction to Geometry, Consisting of Euclid's Elements, Book I ... Euclides Sin vista previa disponible - 2018 |
Términos y frases comunes
AB is equal AC is equal adjacent angles alternate angle angle ABC angle ACB angle AGH angle BAC angle BCD angle equal angles CBA axiom base BC bisects the angle centre circle circumference Constr construction definition describe diagonal Diagram diameter enunciation equal and parallel equal angles equal sides equal to BC EQUIANGULAR POLYGONS equilateral triangle Euclid Euclid's Elements exterior four right angles Geometry given angle given point given straight line greater hypotenuse hypothesis inference isosceles triangle join less Let ABC magnitude meet middle point opposite angles opposite interior angle opposite sides pair of equal parallel to BC parallelogram perpendicular Postulate produced proof Prop proposition prove quadrilateral rectilineal figure respectively equal rhombus right angles right-angled triangle sides equal square supplementary angles theorems thesis trapezium triangle ABC triangles are equal unequal vertex Wherefore
Pasajes populares
Página 132 - 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 86 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 139 - 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 133 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Página 134 - Prove that parallelograms on the same base and between the same parallels are equal in area.
Página 134 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC.
Página 50 - if two straight lines" &c. QED COR. 1. From this it is manifest, that if two straight lines cut one another, the angles which they make at the point where they cut, are together equal to four right angles.
Página 20 - PROB. from a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line : it is required to draw from the point A a straight line equal to BC.
Página 96 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Página 49 - If at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles ; then these two straight lines shall be in one and the same straight line.