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Philip Wood
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"Actioni contrariam semper et æqualem esse reactionem: sive corporum duorum actiones in se mutuo semper esse æquales et in partes contrarias dirigi."

"To every action there is always opposed an equal reaction; or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts." (Mott's translation)

The relevant phrase in Newton's statement is "in partes contrarias dirigi" which translates (unequivocally, I think) as "directed towards contrary parts". "Parts" is used here for the first time in the statement of the law, and it's not clear to me whether Newton meant parts of the interacting bodies (in which case the strong statement seems to be implied) or "parts" meaning places (as in the expression "foreign parts"). The latter would allow the weak interpretation.

Perhaps we should remember that Newton would not have met any clear-cut cases of non-central forces, so he had no obvious motivation for wanting his law to include them (that is to require the weak interpretation). But then Newton could see beyond the obvious...

I conclude that Newton's words are open to interpretation as a statement of the strong law or of the weak law. For most purposes it doesn't matter which, but to answer this question it obviously does. The opening phrase of statement B, "According to Newton's third law", is unsafe. We need to insert "(weak form)" to make the statement clearly true. [Whether or not the law itself, strong or weak, is true is a different matter.]

"Actioni contrariam semper et æqualem esse reactionem: sive corporum duorum actiones in se mutuo semper esse æquales et in partes contrarias dirigi."

"To every action there is always opposed an equal reaction; or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts." (Mott's translation)

The relevant phrase in Newton's statement is "in partes contrarias dirigi" which translates (unequivocally, I think) as "directed towards contrary parts". "Parts" is used here for the first time in the statement of the law, and it's not clear to me whether Newton meant parts of the interacting bodies (in which case the strong statement seems to be implied) or "parts" meaning places (as in the expression "foreign parts"). The latter would allow the weak interpretation.

Perhaps we should remember that Newton would not have met any clear-cut cases of non-central forces, so he had no obvious motivation for wanting his law to include them (that is to require the weak interpretation). But then Newton could see beyond the obvious...

I conclude that the opening phrase of statement B, "According to Newton's third law", is unsafe. We need to insert "(weak form)" to make the statement clearly true. [Whether or not the law itself, strong or weak, is true is a different matter.]

"Actioni contrariam semper et æqualem esse reactionem: sive corporum duorum actiones in se mutuo semper esse æquales et in partes contrarias dirigi."

"To every action there is always opposed an equal reaction; or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts." (Mott's translation)

The relevant phrase in Newton's statement is "in partes contrarias dirigi" which translates (unequivocally, I think) as "directed towards contrary parts". "Parts" is used here for the first time in the statement of the law, and it's not clear to me whether Newton meant parts of the interacting bodies (in which case the strong statement seems to be implied) or "parts" meaning places (as in the expression "foreign parts"). The latter would allow the weak interpretation.

Perhaps we should remember that Newton would not have met any clear-cut cases of non-central forces, so he had no obvious motivation for wanting his law to include them (that is to require the weak interpretation). But then Newton could see beyond the obvious...

I conclude that Newton's words are open to interpretation as a statement of the strong law or of the weak law. For most purposes it doesn't matter which, but to answer this question it obviously does. The opening phrase of statement B, "According to Newton's third law", is unsafe. We need to insert "(weak form)" to make the statement clearly true.

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Philip Wood
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  • 85

"Actioni contrariam semper et æqualem esse reactionem: sive corporum duorum actiones in se mutuo semper esse æquales et in partes contrarias dirigi."

"To every action there is always opposed an equal reaction; or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts." (Mott's translation)

The relevant phrase in Newton's statement is "in partes contrarias dirigi" which translates (unequivocally, I think) as "towards"directed towards contrary parts". "Parts" is used here for the first time in the statement of the law, and it's not clear to me whether Newton meant parts of the interacting bodies (in which case the strong statement seems to be implied) or "parts" meaning places (as in the expression "foreign parts"). The latter would allow the weak interpretation.

Perhaps we should remember that Newton would not have met any clear-cut cases of non-central forces, so he had no obvious motivation for wanting his law to include them (that is to require the weak interpretation). But then Newton could see beyond the obvious...

I conclude that the opening phrase of statement B, "According to Newton's third law", is unsafe. We need to insert "(weak form)" to make the statement clearly true. [Whether or not the law itself, strong or weak, is true is a different matter.]

The relevant phrase in Newton's statement is "in partes contrarias dirigi" which translates (unequivocally, I think) as "towards contrary parts". "Parts" is used here for the first time in the statement of the law, and it's not clear to me whether Newton meant parts of the interacting bodies (in which case the strong statement seems to be implied) or "parts" meaning places (as in the expression "foreign parts"). The latter would allow the weak interpretation.

Perhaps we should remember that Newton would not have met any clear-cut cases of non-central forces, so he had no obvious motivation for wanting his law to include them (that is to require the weak interpretation). But then Newton could see beyond the obvious...

I conclude that the opening phrase of statement B, "According to Newton's third law", is unsafe. We need to insert "(weak form)" to make the statement clearly true. [Whether or not the law itself, strong or weak, is true is a different matter.]

"Actioni contrariam semper et æqualem esse reactionem: sive corporum duorum actiones in se mutuo semper esse æquales et in partes contrarias dirigi."

"To every action there is always opposed an equal reaction; or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts." (Mott's translation)

The relevant phrase in Newton's statement is "in partes contrarias dirigi" which translates (unequivocally, I think) as "directed towards contrary parts". "Parts" is used here for the first time in the statement of the law, and it's not clear to me whether Newton meant parts of the interacting bodies (in which case the strong statement seems to be implied) or "parts" meaning places (as in the expression "foreign parts"). The latter would allow the weak interpretation.

Perhaps we should remember that Newton would not have met any clear-cut cases of non-central forces, so he had no obvious motivation for wanting his law to include them (that is to require the weak interpretation). But then Newton could see beyond the obvious...

I conclude that the opening phrase of statement B, "According to Newton's third law", is unsafe. We need to insert "(weak form)" to make the statement clearly true. [Whether or not the law itself, strong or weak, is true is a different matter.]

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Philip Wood
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The keyrelevant phrase in Newton's statement is "in partes contrarias dirigi" which translates (unequivocally, I think) as "towards contrary parts". "Parts" is used here for the first time in the statement of the law, and it's not clear to me whether Newton meant parts of the interacting bodies (in which case the strong statement seems to be implied) or "parts" meaning places (as in the expression "foreign parts"). The latter would allow the weak interpretation.

Perhaps we should remember that Newton would not have met any clear-cut cases of non-central forces, so he had no obvious motivation for wanting his law to include them (that is to require the weak interpretation). But then Newton could see beyond the obvious...

I conclude that the opening phrase of statement B, "According to Newton's third law", is unsafe. We need to insert "(weak form)" to make the statement clearly true. [Whether or not the law itself, strong or weak, is true is a different matter.]

The key phrase in Newton's statement is "in partes contrarias dirigi" which translates (unequivocally, I think) as "towards contrary parts". "Parts" is used here for the first time in the statement of the law, and it's not clear to me whether Newton meant parts of the interacting bodies (in which case the strong statement seems to be implied) or "parts" meaning places (as in the expression "foreign parts"). The latter would allow the weak interpretation.

Perhaps we should remember that Newton would not have met any clear-cut cases of non-central forces, so he had no obvious motivation for wanting his law to include them (that is to require the weak interpretation). But then Newton could see beyond the obvious...

I conclude that the opening phrase of statement B, "According to Newton's third law", is unsafe. We need to insert "(weak form)" to make the statement clearly true. [Whether or not the law itself, strong or weak, is true is a different matter.]

The relevant phrase in Newton's statement is "in partes contrarias dirigi" which translates (unequivocally, I think) as "towards contrary parts". "Parts" is used here for the first time in the statement of the law, and it's not clear to me whether Newton meant parts of the interacting bodies (in which case the strong statement seems to be implied) or "parts" meaning places (as in the expression "foreign parts"). The latter would allow the weak interpretation.

Perhaps we should remember that Newton would not have met any clear-cut cases of non-central forces, so he had no obvious motivation for wanting his law to include them (that is to require the weak interpretation). But then Newton could see beyond the obvious...

I conclude that the opening phrase of statement B, "According to Newton's third law", is unsafe. We need to insert "(weak form)" to make the statement clearly true. [Whether or not the law itself, strong or weak, is true is a different matter.]

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Philip Wood
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